@article {AKMW, AUTHOR = {Abramovich, Dan and Karu, Kalle and Matsuki, Kenji and W{\l}odarczyk, Jaros{\l}aw}, TITLE = {Torification and factorization of birational maps}, JOURNAL = {J. Amer. Math. Soc.}, FJOURNAL = {Journal of the American Mathematical Society}, VOLUME = {15}, YEAR = {2002}, NUMBER = {3}, PAGES = {531--572}, ISSN = {0894-0347}, MRCLASS = {14E05 (14E15 14L24)}, MRNUMBER = {1896232}, MRREVIEWER = {Alexandr V. Pukhlikov}, DOI = {10.1090/S0894-0347-02-00396-X}, URL = {https://doi.org/10.1090/S0894-0347-02-00396-X}, } @article {ACMV2, AUTHOR = {Jeffrey D. Achter and Sebastian Casalaina-Martin and Charles Vial}, TITLE = {Distinguished models of intermediate Jacobians}, YEAR = {2018}, JOURNAL = {Journal of the Institute of Mathematics of Jussieu}, DOI = { 10.1017/S1474748018000245}, VOLUME ={to appear}, } @article {ACMV1, AUTHOR = {Achter, Jeffrey D. and Casalaina-Martin, Sebastian and Vial, Charles}, TITLE = {On descending cohomology geometrically}, JOURNAL = {Compos. Math.}, FJOURNAL = {Compositio Mathematica}, VOLUME = {153}, YEAR = {2017}, NUMBER = {7}, PAGES = {1446--1478}, ISSN = {0010-437X}, MRCLASS = {11G35 (11G10 14C25 14C30 14K30)}, MRNUMBER = {3705264}, MRREVIEWER = {Fumio Hazama}, DOI = {10.1112/S0010437X17007151}, URL = {https://doi.org/10.1112/S0010437X17007151}, } @article {AK, AUTHOR = {Altman, Allen B. and Kleiman, Steven L.}, TITLE = {Foundations of the theory of {F}ano schemes}, JOURNAL = {Compositio Math.}, FJOURNAL = {Compositio Mathematica}, VOLUME = {34}, YEAR = {1977}, NUMBER = {1}, PAGES = {3--47}, ISSN = {0010-437X}, MRCLASS = {14C05 (14C20 14M15 14N10)}, MRNUMBER = {0569043}, MRREVIEWER = {Joel Roberts}, URL = {http://www.numdam.org/item?id=CM_1977__34_1_3_0}, } @phdthesis {amer, AUTHOR = { M. Amer}, TITLE = {Quadratische {F}ormen \"{u}ber {F}unktionenk\"{o}rpern}, SCHOOl = { Johannes Gutenberg Universit\"{a}t, Mainz}, YEAR = {1976}, } @article {AsIn, AUTHOR = {Asgarli, Shamil and Inchiostro, Giovanni}, TITLE = {The {P}icard group of the moduli of smooth complete intersections of two quadrics}, NOTE = {{\tt arXiv:1710.10113}}, JOURNAL = {Trans. Amer. Math. Soc.}, FJOURNAL = {Transactions of the American Mathematical Society}, YEAR = {2017}, } @misc{BW, title={Intermediate {J}acobians and rationality over arbitrary fields}, author={Olivier Benoist and Olivier Wittenberg}, year={2019}, note={\texttt{arXiv:1909.12668}}, } @article {BenWit, AUTHOR = {Benoist, Olivier and Wittenberg, Olivier}, TITLE = {The {C}lemens-{G}riffiths method over non-closed fields}, JOURNAL = {Algebr. Geom.}, FJOURNAL = {Algebraic Geometry}, VOLUME = {7}, YEAR = {2020}, NUMBER = {6}, PAGES = {696--721}, ISSN = {2313-1691}, MRCLASS = {14E08 (14G27 14K30)}, MRNUMBER = {4156423}, DOI = {10.14231/ag-2020-025}, URL = {https://doi.org/10.14231/ag-2020-025}, } @article {Bertram, AUTHOR = {Bertram, Aaron}, TITLE = {Moduli of rank-{$2$} vector bundles, theta divisors, and the geometry of curves in projective space}, JOURNAL = {J. Differential Geom.}, FJOURNAL = {Journal of Differential Geometry}, VOLUME = {35}, YEAR = {1992}, NUMBER = {2}, PAGES = {429--469}, ISSN = {0022-040X}, MRCLASS = {14H60 (14D20)}, MRNUMBER = {1158344}, MRREVIEWER = {Arnaud Beauville}, URL = {http://projecteuclid.org/euclid.jdg/1214448083}, } @article {BGW, AUTHOR = {Bhargava, Manjul and Gross, Benedict H. and Wang, Xiaoheng}, TITLE = {A positive proportion of locally soluble hyperelliptic curves over {$\mathbb Q$} have no point over any odd degree extension}, NOTE = {With an appendix by Tim Dokchitser and Vladimir Dokchitser}, JOURNAL = {J. Amer. Math. Soc.}, FJOURNAL = {Journal of the American Mathematical Society}, VOLUME = {30}, YEAR = {2017}, NUMBER = {2}, PAGES = {451--493}, ISSN = {0894-0347}, MRCLASS = {11G30 (14G05 14H50)}, MRNUMBER = {3600041}, MRREVIEWER = {James H. Stankewicz}, DOI = {10.1090/jams/863}, URL = {https://doi.org/10.1090/jams/863}, } @article {BSD, AUTHOR = {Birch, B. J. and Swinnerton-Dyer, H. P. F.}, TITLE = {The {H}asse problem for rational surfaces}, NOTE = {Collection of articles dedicated to Helmut Hasse on his seventy-fifth birthday, III}, JOURNAL = {J. Reine Angew. Math.}, FJOURNAL = {Journal f\"{u}r die Reine und Angewandte Mathematik}, VOLUME = {274/275}, YEAR = {1975}, PAGES = {164--174}, ISSN = {0075-4102}, MRCLASS = {14J20 (14G25 10C20)}, MRNUMBER = {0429913}, MRREVIEWER = {D. J. Lewis}, DOI = {10.1515/crll.1975.274-275.164}, URL = {https://doi.org/10.1515/crll.1975.274-275.164}, } @article {Brumer, AUTHOR = {Brumer, Armand}, TITLE = {Remarques sur les couples de formes quadratiques}, JOURNAL = {C. R. Acad. Sci. Paris S\'{e}r. A-B}, VOLUME = {286}, YEAR = {1978}, NUMBER = {16}, PAGES = {A679--A681}, MRCLASS = {10C05 (14G05)}, MRNUMBER = {0498374}, } @inproceedings{CTm, AUTHOR = {J.-L. Colliot-Th\'el\`ene}, TITLE = { Non rationalit\'e stable d'hypersurfaces cubiques sur des corps non alg\'ebriquement clos}, BOOKTITLE = { {\it K-Theory}, Proceedings of the International Colloquium, Mumbai, 2016}, PUBLISHER = {Hindustan Book Agency}, YEAR = {2018}, PAGES = {349--366}, } @article {CTCS, AUTHOR = {Colliot-Th\'{e}l\`ene, Jean-Louis and Coray, Daniel and Sansuc, Jean-Jacques}, TITLE = {Descente et principe de {H}asse pour certaines vari\'{e}t\'{e}s rationnelles}, JOURNAL = {J. Reine Angew. Math.}, FJOURNAL = {Journal f\"{u}r die Reine und Angewandte Mathematik}, VOLUME = {320}, YEAR = {1980}, PAGES = {150--191}, ISSN = {0075-4102}, MRCLASS = {14G05 (10C02)}, MRNUMBER = {592151}, MRREVIEWER = {A. Pfister}, } @article {CTSSDI, AUTHOR = {Colliot-Th\'el\`ene, Jean-Louis and Sansuc, Jean-Jacques and Swinnerton-Dyer, Peter}, TITLE = {Intersections of two quadrics and {C}h\^atelet surfaces. {I}}, JOURNAL = {J. Reine Angew. Math.}, FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik. [Crelle's Journal]}, VOLUME = {373}, YEAR = {1987}, PAGES = {37--107}, ISSN = {0075-4102}, MRCLASS = {11G35 (11E81 14J20 14J26)}, MRNUMBER = {870307}, MRREVIEWER = {Noriko Yui}, } @article {CTSSDII, AUTHOR = {Colliot-Th\'el\`ene, Jean-Louis and Sansuc, Jean-Jacques and Swinnerton-Dyer, Peter}, TITLE = {Intersections of two quadrics and {C}h\^atelet surfaces. {II}}, JOURNAL = {J. Reine Angew. Math.}, FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik. [Crelle's Journal]}, VOLUME = {374}, YEAR = {1987}, PAGES = {72--168}, ISSN = {0075-4102}, MRCLASS = {11G35 (11E81 14J20 14J26)}, MRNUMBER = {876222}, MRREVIEWER = {Noriko Yui}, } @inproceedings{ct-surve, author = {Colliot-Th{\'e}l{\`e}ne, Jean-Louis}, title = {Non rationalit\'e stable sur les corps quelconques}, pages = {73--110}, year = {2019}, booktitle = {Birational Geometry of Hypersurfaces, Gargnano del Garda, Italy, 2018}, series = {Lecture Notes of the Unione Matematica Italiana}, Editor = { Andreas Hochenegger and Manfred Lehn and Paolo Stellari}, Publisher = {Springer International Publishing}, } @incollection {CTS, AUTHOR = {Colliot-Th\'{e}l\`ene, J.-L. and Sansuc, J.-J.}, TITLE = {La descente sur les vari\'{e}t\'{e}s rationnelles}, BOOKTITLE = {Journ\'{e}es de {G}\'{e}ometrie {A}lg\'{e}brique d'{A}ngers, {J}uillet 1979/{A}lgebraic {G}eometry, {A}ngers, 1979}, PAGES = {223--237}, PUBLISHER = {Sijthoff \& Noordhoff, Alphen aan den Rijn---Germantown, Md.}, YEAR = {1980}, MRCLASS = {14G05 (14C15)}, MRNUMBER = {605344}, MRREVIEWER = {Daniel Coray}, } @article {ct-pirutka, AUTHOR = {Colliot-Th{\'e}l{\`e}ne, Jean-Louis and Pirutka, Alena}, TITLE = {Hypersurfaces quartiques de dimension 3: non-rationalit\'e stable}, JOURNAL = {Ann. Sci. \'Ec. Norm. Sup\'er. (4)}, FJOURNAL = {Annales Scientifiques de l'\'Ecole Normale Sup\'erieure. Quatri\`eme S\'erie}, VOLUME = {49}, YEAR = {2016}, NUMBER = {2}, PAGES = {371--397}, ISSN = {0012-9593}, MRCLASS = {14G25 (14Cxx)}, MRNUMBER = {3481353}, } @article {Dale, AUTHOR = {Dale, M.}, TITLE = {Terracini's lemma and the secant variety of a curve}, JOURNAL = {Proc. London Math. Soc. (3)}, FJOURNAL = {Proceedings of the London Mathematical Society. Third Series}, VOLUME = {49}, YEAR = {1984}, NUMBER = {2}, PAGES = {329--339}, ISSN = {0024-6115}, MRCLASS = {14N10 (14E22)}, MRNUMBER = {748993}, MRREVIEWER = {D. Gallarati}, DOI = {10.1112/plms/s3-49.2.329}, URL = {https://doi.org/10.1112/plms/s3-49.2.329}, } @article {DebMan, AUTHOR = {Debarre, Olivier and Manivel, Laurent}, TITLE = {Sur la vari\'{e}t\'{e} des espaces lin\'{e}aires contenus dans une intersection compl\`ete}, JOURNAL = {Math. Ann.}, FJOURNAL = {Mathematische Annalen}, VOLUME = {312}, YEAR = {1998}, NUMBER = {3}, PAGES = {549--574}, ISSN = {0025-5831}, MRCLASS = {14M15 (14J40)}, MRNUMBER = {1654757}, MRREVIEWER = {Yuri G. Prokhorov}, DOI = {10.1007/s002080050235}, URL = {https://doi.org/10.1007/s002080050235}, } @book {DIK, AUTHOR = {Degtyarev, A. and Itenberg, I. and Kharlamov, V.}, TITLE = {Real {E}nriques surfaces}, SERIES = {Lecture Notes in Mathematics}, VOLUME = {1746}, PUBLISHER = {Springer-Verlag, Berlin}, YEAR = {2000}, PAGES = {xvi+259}, ISBN = {3-540-41088-0}, MRCLASS = {14P05 (14J28)}, MRNUMBER = {1795406}, MRREVIEWER = {Sergey M. Finashin}, DOI = {10.1007/BFb0103960}, URL = {https://doi.org/10.1007/BFb0103960}, } @article {DR, AUTHOR = {Desale, U. V. and Ramanan, S.}, TITLE = {Classification of vector bundles of rank {$2$} on hyperelliptic curves}, JOURNAL = {Invent. Math.}, FJOURNAL = {Inventiones Mathematicae}, VOLUME = {38}, YEAR = {1976/77}, NUMBER = {2}, PAGES = {161--185}, ISSN = {0020-9910}, MRCLASS = {14F05 (14D20)}, MRNUMBER = {0429897}, MRREVIEWER = {P. E. Newstead}, DOI = {10.1007/BF01408570}, URL = {https://doi.org/10.1007/BF01408570}, } @book {EKM, AUTHOR = {Elman, Richard and Karpenko, Nikita and Merkurjev, Alexander}, TITLE = {The algebraic and geometric theory of quadratic forms}, SERIES = {American Mathematical Society Colloquium Publications}, VOLUME = {56}, PUBLISHER = {American Mathematical Society, Providence, RI}, YEAR = {2008}, PAGES = {viii+435}, ISBN = {978-0-8218-4329-1}, MRCLASS = {11Exx (11-02 11E04 11E81 14C15 14C25)}, MRNUMBER = {2427530}, MRREVIEWER = {Andrzej S\l adek}, DOI = {10.1090/coll/056}, URL = {https://doi.org/10.1090/coll/056}, } @book {Fulton, AUTHOR = {Fulton, William}, TITLE = {Intersection theory}, SERIES = {Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics}, VOLUME = {2}, EDITION = {Second}, PUBLISHER = {Springer-Verlag, Berlin}, YEAR = {1998}, PAGES = {xiv+470}, ISBN = {3-540-62046-X; 0-387-98549-2}, MRCLASS = {14C17 (14-02)}, MRNUMBER = {1644323}, DOI = {10.1007/978-1-4612-1700-8}, URL = {https://doi.org/10.1007/978-1-4612-1700-8}, } @article {HKT-conic, AUTHOR = {Hassett, Brendan and Kresch, Andrew and Tschinkel, Yuri}, TITLE = {Stable rationality and conic bundles}, JOURNAL = {Math. Ann.}, FJOURNAL = {Mathematische Annalen}, VOLUME = {365}, YEAR = {2016}, NUMBER = {3-4}, PAGES = {1201--1217}, ISSN = {0025-5831}, MRCLASS = {Preliminary Data}, MRNUMBER = {3521088}, DOI = {10.1007/s00208-015-1292-y}, URL = {http://dx.doi.org/10.1007/s00208-015-1292-y}, } @article {HPT16, AUTHOR = {Hassett, Brendan and Pirutka, Alena and Tschinkel, Yuri}, TITLE = {Stable rationality of quadric surface bundles over surfaces}, JOURNAL = {Acta Math.}, FJOURNAL = {Acta Mathematica}, VOLUME = {220}, YEAR = {2018}, NUMBER = {2}, PAGES = {341--365}, ISSN = {0001-5962}, MRCLASS = {14E08 (14D06)}, MRNUMBER = {3849287}, } @misc {HPT17, AUTHOR = {Hassett, Brendan and Pirutka, Alena and Tschinkel, Yuri}, TITLE = {Intersections of three quadrics in {$\Bbb P^7$}}, BOOKTITLE = {Surveys in differential geometry 2017. {C}elebrating the 50th anniversary of the {J}ournal of {D}ifferential {G}eometry}, SERIES = {Surv. Differ. Geom.}, VOLUME = {22}, PAGES = {259--274}, PUBLISHER = {Int. Press, Somerville, MA}, YEAR = {2018}, MRCLASS = {14E08 (14M10)}, MRNUMBER = {3838120}, NOTE = {{\tt arXiv:1706.01371}}, } @article {HT-fano, AUTHOR = {Hassett, Brendan and Tschinkel, Yuri}, TITLE = {On stable rationality of {F}ano threefolds and del {P}ezzo fibrations}, JOURNAL = {J. Reine Angew. Math.}, FJOURNAL = {Journal f\"{u}r die Reine und Angewandte Mathematik. [Crelle's Journal]}, VOLUME = {751}, YEAR = {2019}, PAGES = {275--287}, ISSN = {0075-4102}, MRCLASS = {14E05 (14J45)}, MRNUMBER = {3956696}, DOI = {10.1515/crelle-2016-0058}, URL = {https://doi.org/10.1515/crelle-2016-0058}, } @misc {HT, author = {Hassett, Brendan and Tschinkel, Yuri}, title = {Rationality of complete intersections of two quadrics}, note = {{\tt arXiv:1903.08979v1}}, year = {2019}, } @article{HTCPAM, title={Cycle class maps and birational invariants}, author={Brendan Hassett and Yuri Tschinkel}, JOURNAL = {Comm. Pure Appl. Math.}, FJOURNAL = {Communications on Pure and Applied Mathematics}, VOLUME = {to appear}, year={2019}, note={\texttt{arXiv:1908.00406}}, doi = {https://doi.org/10.1002/cpa.21967}, } @incollection {H-I, AUTHOR = {Iskovskikh, V. A. and Prokhorov, Yu. G.}, TITLE = {Fano varieties}, BOOKTITLE = {Algebraic geometry, {V}}, SERIES = {Encyclopaedia Math. Sci.}, VOLUME = {47}, PAGES = {1--247}, PUBLISHER = {Springer, Berlin}, YEAR = {1999}, MRCLASS = {14J45 (14E07 14F22 14K30)}, MRNUMBER = {1668579}, MRREVIEWER = {Takao Fujita}, } @article {KollarNash, AUTHOR = {Koll\'{a}r, J\'{a}nos}, TITLE = {The {N}ash conjecture for threefolds}, JOURNAL = {Electron. Res. Announc. Amer. Math. Soc.}, FJOURNAL = {Electronic Research Announcements of the American Mathematical Society}, VOLUME = {4}, YEAR = {1998}, PAGES = {63--73}, ISSN = {1079-6762}, MRCLASS = {57N10 (14J30 14P05)}, MRNUMBER = {1641168}, MRREVIEWER = {A. Tognoli}, DOI = {10.1090/S1079-6762-98-00049-3}, URL = {https://doi.org/10.1090/S1079-6762-98-00049-3}, } @article {KT, AUTHOR = {Kontsevich, Maxim and Tschinkel, Yuri}, TITLE = {Specialization of birational types}, JOURNAL = {Invent. Math.}, FJOURNAL = {Inventiones Mathematicae}, VOLUME = {217}, YEAR = {2019}, NUMBER = {2}, PAGES = {415--432}, ISSN = {0020-9910}, MRCLASS = {14E08}, MRNUMBER = {3987175}, DOI = {10.1007/s00222-019-00870-9}, URL = {https://doi.org/10.1007/s00222-019-00870-9}, } @article {Krasnov, AUTHOR = {Krasnov, V. A.}, TITLE = {On the intersection of two real quadrics}, JOURNAL = {Izv. Ross. Akad. Nauk Ser. Mat.}, FJOURNAL = {Rossi\u{\i}skaya Akademiya Nauk. Izvestiya. Seriya Matematicheskaya}, VOLUME = {82}, YEAR = {2018}, NUMBER = {1}, PAGES = {97--150}, ISSN = {1607-0046}, MRCLASS = {14P25 (14M10 14N25 57R19)}, MRNUMBER = {3749598}, MRREVIEWER = {Sergey M. Finashin}, DOI = {10.4213/im8535}, URL = {https://doi.org/10.4213/im8535}, } @article {krylov-okada, AUTHOR = {Krylov, Igor and Okada, Takuzo}, TITLE = {Stable {R}ationality of del {P}ezzo {F}ibrations of {L}ow {D}egree {O}ver {P}rojective {S}paces}, JOURNAL = {Int. Math. Res. Not. IMRN}, FJOURNAL = {International Mathematics Research Notices. IMRN}, YEAR = {2020}, NUMBER = {23}, PAGES = {9075--9119}, ISSN = {1073-7928}, MRCLASS = {14J26 (14D06)}, MRNUMBER = {4182791}, DOI = {10.1093/imrn/rny252}, URL = {https://doi.org/10.1093/imrn/rny252}, } @incollection {kun, AUTHOR = {Kunyavski\u\i , B. \`E.}, TITLE = {Three-dimensional algebraic tori}, BOOKTITLE = {Investigations in number theory ({R}ussian)}, PAGES = {90--111}, NOTE = {Translated in Selecta Math. Soviet. {{\bf{9}}} (1990), no. 1, 1--21}, PUBLISHER = {Saratov. Gos. Univ., Saratov}, YEAR = {1987}, MRCLASS = {14M25 (20G15)}, MRNUMBER = {1032541}, MRREVIEWER = {Vladimir L. Popov}, } @misc{KP, title={Rationality of {F}ano threefolds over non-closed fields}, author={Alexander Kuznetsov and Yuri Prokhorov}, year={2020}, note={\texttt{arXiv:1911.08949}}, } @book {lam, AUTHOR = {Lam, T. Y.}, TITLE = {The algebraic theory of quadratic forms}, NOTE = {Mathematics Lecture Note Series}, PUBLISHER = {W. A. Benjamin, Inc., Reading, Mass.}, YEAR = {1973}, PAGES = {xi+344}, MRCLASS = {10C05 (15A63)}, MRNUMBER = {0396410}, MRREVIEWER = {J. S. Hsia}, } @article {LangFF, AUTHOR = {Lang, Serge}, TITLE = {Abelian varieties over finite fields}, JOURNAL = {Proc. Nat. Acad. Sci. U.S.A.}, FJOURNAL = {Proceedings of the National Academy of Sciences of the United States of America}, VOLUME = {41}, YEAR = {1955}, PAGES = {174--176}, ISSN = {0027-8424}, MRCLASS = {14.0X}, MRNUMBER = {0071115}, MRREVIEWER = {P. Samuel}, DOI = {10.1073/pnas.41.3.174}, URL = {https://doi.org/10.1073/pnas.41.3.174}, } @misc {leep, AUTHOR = {D. Leep}, TITLE = {The {A}mer--{B}rumer theorem over arbitrary fields}, NOTE = {\url{http://www.ms.uky.edu/~leep/Preprints.html}}, } @article {manin-ts, AUTHOR = {Manin, Yu. I. and Tsfasman, M. A.}, TITLE = {Rational varieties: algebra, geometry, arithmetic}, JOURNAL = {Uspekhi Mat. Nauk}, FJOURNAL = {Akademiya Nauk SSSR i Moskovskoe Matematicheskoe Obshchestvo. Uspekhi Matematicheskikh Nauk}, VOLUME = {41}, YEAR = {1986}, NUMBER = {2(248)}, PAGES = {43--94}, ISSN = {0042-1316}, MRCLASS = {11G35 (14G05 14J20)}, MRNUMBER = {842161}, MRREVIEWER = {Daniel Coray}, } @article {ManinIHES, AUTHOR = {Manin, Ju. I.}, TITLE = {Rational surfaces over perfect fields}, JOURNAL = {Inst. Hautes \'Etudes Sci. Publ. Math.}, FJOURNAL = {Institut des Hautes \'Etudes Scientifiques. Publications Math\'ematiques}, NUMBER = {30}, YEAR = {1966}, PAGES = {55--113}, ISSN = {0073-8301}, MRCLASS = {14.20}, MRNUMBER = {0225780}, MRREVIEWER = {M. L. Laplaza}, NOTE = {English translation: American Mathematical Society Translations, Ser. 2, Vol. 84 (1969): Twelve papers on algebra, algebraic geometry and topology}, } @article {NS, AUTHOR = {Nicaise, Johannes and Shinder, Evgeny}, TITLE = {The motivic nearby fiber and degeneration of stable rationality}, JOURNAL = {Invent. Math.}, FJOURNAL = {Inventiones Mathematicae}, VOLUME = {217}, YEAR = {2019}, NUMBER = {2}, PAGES = {377--413}, ISSN = {0020-9910}, MRCLASS = {14E08 (14C35)}, MRNUMBER = {3987174}, DOI = {10.1007/s00222-019-00869-2}, URL = {https://doi.org/10.1007/s00222-019-00869-2}, } @incollection {PirSurvey, AUTHOR = {Pirutka, Alena}, TITLE = {Varieties that are not stably rational, zero-cycles and unramified cohomology}, BOOKTITLE = {Algebraic geometry: {S}alt {L}ake {C}ity 2015}, SERIES = {Proc. Sympos. Pure Math.}, VOLUME = {97}, PAGES = {459--483}, PUBLISHER = {Amer. Math. Soc., Providence, RI}, YEAR = {2018}, MRCLASS = {14E08 (14C25 14F22)}, MRNUMBER = {3821181}, } @phdthesis {ReidThesis, AUTHOR = {Reid, Miles}, TITLE = {The complete intersection of two or more quadrics}, YEAR = {1972}, SCHOOL = {Cambridge University}, } @article {schrei, AUTHOR = {Schreieder, Stefan}, TITLE = {Quadric surface bundles over surfaces and stable rationality}, JOURNAL = {Algebra Number Theory}, FJOURNAL = {Algebra \& Number Theory}, VOLUME = {12}, YEAR = {2018}, NUMBER = {2}, PAGES = {479--490}, ISSN = {1937-0652}, MRCLASS = {14E08 (14D06 14F22 14J35 14M20)}, MRNUMBER = {3803711}, MRREVIEWER = {Dori Bejleri}, DOI = {10.2140/ant.2018.12.479}, URL = {https://doi.org/10.2140/ant.2018.12.479}, } @article {SerreLauter, AUTHOR = {Lauter, Kristin}, TITLE = {Geometric methods for improving the upper bounds on the number of rational points on algebraic curves over finite fields}, NOTE = {With an appendix in French by J.-P. Serre}, JOURNAL = {J. Algebraic Geom.}, FJOURNAL = {Journal of Algebraic Geometry}, VOLUME = {10}, YEAR = {2001}, NUMBER = {1}, PAGES = {19--36}, ISSN = {1056-3911}, MRCLASS = {11G20 (14G10 14G15)}, MRNUMBER = {1795548}, MRREVIEWER = {Gabriel D. Villa-Salvador}, } @article {Shen, AUTHOR = {Shen, Mingmin}, TITLE = {On relations among 1-cycles on cubic hypersurfaces}, JOURNAL = {J. Algebraic Geom.}, FJOURNAL = {Journal of Algebraic Geometry}, VOLUME = {23}, YEAR = {2014}, NUMBER = {3}, PAGES = {539--569}, ISSN = {1056-3911}, MRCLASS = {14C25 (14C05 14C15)}, MRNUMBER = {3205590}, MRREVIEWER = {Michele Rossi}, DOI = {10.1090/S1056-3911-2014-00631-7}, URL = {https://doi.org/10.1090/S1056-3911-2014-00631-7}, } @article {Thompson, AUTHOR = {Thompson, Robert C.}, TITLE = {Pencils of complex and real symmetric and skew matrices}, JOURNAL = {Linear Algebra Appl.}, FJOURNAL = {Linear Algebra and its Applications}, VOLUME = {147}, YEAR = {1991}, PAGES = {323--371}, ISSN = {0024-3795}, MRCLASS = {15A21 (15A54)}, MRNUMBER = {1088668}, MRREVIEWER = {Anna Lee}, DOI = {10.1016/0024-3795(91)90238-R}, URL = {https://doi.org/10.1016/0024-3795(91)90238-R}, } @article {Tjurin, AUTHOR = {Tjurin, A. N.}, TITLE = {The intersection of quadrics}, JOURNAL = {Uspehi Mat. Nauk}, FJOURNAL = {Akademiya Nauk SSSR i Moskovskoe Matematicheskoe Obshchestvo. Uspekhi Matematicheskikh Nauk}, VOLUME = {30}, YEAR = {1975}, NUMBER = {6(186)}, PAGES = {51--99}, ISSN = {0042-1316}, MRCLASS = {14K30 (14M10 14N05)}, MRNUMBER = {0424833}, MRREVIEWER = {Miles Reid}, } @article {voisin, AUTHOR = {Voisin, Claire}, TITLE = {Unirational threefolds with no universal codimension {$2$} cycle}, JOURNAL = {Invent. Math.}, FJOURNAL = {Inventiones Mathematicae}, VOLUME = {201}, YEAR = {2015}, NUMBER = {1}, PAGES = {207--237}, ISSN = {0020-9910}, MRCLASS = {14M20 (14E08 14F45 14J30 14K30)}, MRNUMBER = {3359052}, MRREVIEWER = {M. Kh. Gizatullin}, DOI = {10.1007/s00222-014-0551-y}, URL = {http://dx.doi.org/10.1007/s00222-014-0551-y}, } @incollection {Voisin-survey, AUTHOR = {Voisin, Claire}, TITLE = {Stable birational invariants and the {L}\"{u}roth problem}, BOOKTITLE = {Surveys in differential geometry 2016. {A}dvances in geometry and mathematical physics}, SERIES = {Surv. Differ. Geom.}, VOLUME = {21}, PAGES = {313--342}, PUBLISHER = {Int. Press, Somerville, MA}, YEAR = {2016}, MRCLASS = {14E08 (14C15)}, MRNUMBER = {3525100}, MRREVIEWER = {Kieran G. O'Grady}, } @article {vosk, AUTHOR = {Voskresenskii, V. E.}, TITLE = {Galois lattices and algebraic groups}, NOTE = {Pontryagin Conference, 8, Algebra (Moscow, 1998)}, JOURNAL = {J. Math. Sci. (New York)}, FJOURNAL = {Journal of Mathematical Sciences (New York)}, VOLUME = {106}, YEAR = {2001}, NUMBER = {4}, PAGES = {3098--3144}, ISSN = {1072-3374}, MRCLASS = {14L15 (14M25 20G15)}, MRNUMBER = {1871136}, MRREVIEWER = {Boris \`E. Kunyavski\u\i }, DOI = {10.1023/A:1011330704163}, URL = {https://doi.org/10.1023/A:1011330704163}, } @article {wang, AUTHOR = {Wang, Xiaoheng}, TITLE = {Maximal linear spaces contained in the base loci of pencils of quadrics}, JOURNAL = {Algebr. Geom.}, FJOURNAL = {Algebraic Geometry}, VOLUME = {5}, YEAR = {2018}, NUMBER = {3}, PAGES = {359--397}, ISSN = {2214-2584}, MRCLASS = {14H40 (14J45 14N20)}, MRNUMBER = {3800357}, DOI = {10.14231/AG-2018-011}, URL = {https://doi.org/10.14231/AG-2018-011}, }