\begin{thebibliography}{ACMV19b}

\bibitem[ACMV18]{ACMV2}
Jeffrey~D. Achter, Sebastian Casalaina-Martin, and Charles Vial.
\newblock Distinguished models of intermediate {J}acobians.
\newblock {\em J. Inst. Math. Jussieu}, 2018.

\bibitem[ACMV19a]{ACMV19}
Jeffrey~D. Achter, Sebastian Casalaina-Martin, and Charles Vial.
\newblock A functorial approach to regular homomorphisms, 2019.
\newblock \texttt{arXiv:1911.09911}.

\bibitem[ACMV19b]{ACMV18}
Jeffrey~D. Achter, Sebastian Casalaina-Martin, and Charles Vial.
\newblock Normal functions for algebraically trivial cycles are algebraic for
  arithmetic reasons.
\newblock {\em Forum Math. Sigma}, 7:e36, 22, 2019.
\newblock \texttt{arXiv:1810.07404}.

\bibitem[AKW17]{AKW}
Benjamin Antieau, Daniel Krashen, and Matthew Ward.
\newblock Derived categories of torsors for abelian schemes.
\newblock {\em Adv. Math.}, 306:1--23, 2017.

\bibitem[BGW17]{BGW}
Manjul Bhargava, Benedict~H. Gross, and Xiaoheng Wang.
\newblock A positive proportion of locally soluble hyperelliptic curves over
  {$\Bbb Q$} have no point over any odd degree extension.
\newblock {\em J. Amer. Math. Soc.}, 30(2):451--493, 2017.
\newblock With an appendix by Tim Dokchitser and Vladimir Dokchitser.

\bibitem[Blo79]{Bloch}
S.~Bloch.
\newblock Torsion algebraic cycles and a theorem of {R}oitman.
\newblock {\em Compositio Math.}, 39(1):107--127, 1979.

\bibitem[BS83]{BlSr}
S.~Bloch and V.~Srinivas.
\newblock Remarks on correspondences and algebraic cycles.
\newblock {\em Amer. J. Math.}, 105(5):1235--1253, 1983.

\bibitem[BW19a]{BenWit}
Olivier Benoist and Olivier Wittenberg.
\newblock The {C}lemens-{G}riffiths method over non-closed fields.
\newblock {\em Algebr. Geom.}, to appear, 2019.
\newblock \texttt{arXiv:1903.08015}.

\bibitem[BW19b]{BenWit2}
Olivier Benoist and Olivier Wittenberg.
\newblock Intermediate {J}acobians and rationality over arbitrary fields, 2019.
\newblock \texttt{arXiv:1909.12668}.

\bibitem[Car87]{Carlson}
James~A. Carlson.
\newblock The geometry of the extension class of a mixed {H}odge structure.
\newblock In {\em Algebraic geometry, {B}owdoin, 1985 ({B}runswick, {M}aine,
  1985)}, volume~46 of {\em Proc. Sympos. Pure Math.}, pages 199--222. Amer.
  Math. Soc., Providence, RI, 1987.

\bibitem[Con17]{Conrad}
Brian Conrad.
\newblock Albanese variety over non-perfect fields, 2017.
\newblock Available at
  \url{https://mathoverflow.net/questions/260982/albanese-variety-over-non-perfect-fields}.

\bibitem[DM98]{DebMan}
Olivier Debarre and Laurent Manivel.
\newblock Sur la vari\'{e}t\'{e} des espaces lin\'{e}aires contenus dans une
  intersection compl\`ete.
\newblock {\em Math. Ann.}, 312(3):549--574, 1998.

\bibitem[EV88]{EV}
H\'{e}l\`ene Esnault and Eckart Viehweg.
\newblock Deligne-{B}e\u{\i}linson cohomology.
\newblock In {\em Be\u{\i}linson's conjectures on special values of
  {$L$}-functions}, volume~4 of {\em Perspect. Math.}, pages 43--91. Academic
  Press, Boston, MA, 1988.

\bibitem[Ful98]{Fulton}
William Fulton.
\newblock {\em Intersection theory}, volume~2 of {\em Ergebnisse der Mathematik
  und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics}.
\newblock Springer-Verlag, Berlin, second edition, 1998.

\bibitem[Gri69]{GriffithsAnnals}
Phillip~A. Griffiths.
\newblock On the periods of certain rational integrals. {I}, {II}.
\newblock {\em Ann. of Math. (2) 90 (1969), 460-495; ibid. (2)}, 90:496--541,
  1969.

\bibitem[Gri70]{GriffithsIHES}
Phillip~A. Griffiths.
\newblock Periods of integrals on algebraic manifolds. {III}. {S}ome global
  differential-geometric properties of the period mapping.
\newblock {\em Inst. Hautes \'{E}tudes Sci. Publ. Math.}, (38):125--180, 1970.

\bibitem[GT80]{GrTr}
Silvio Greco and C.~Traverso.
\newblock On seminormal schemes.
\newblock {\em Compositio Mathematica}, 40(3):325--365, 1980.

\bibitem[HL18]{HasLai}
Brendan Hassett and Kuan-Wen Lai.
\newblock Cremona transformations and derived equivalences of {K}3 surfaces.
\newblock {\em Compos. Math.}, 154(7):1508--1533, 2018.

\bibitem[HT19]{HT2quad}
Brendan Hassett and Yuri Tschinkel.
\newblock Rationality of complete intersections of two quadrics, 2019.
\newblock \texttt{arXiv:1903.08979}, with an appendix by {J}.-{L}.
  {C}olliot-{T}h\'el\`ene.

\bibitem[IP99]{IP}
V.~A. Iskovskikh and Yu.~G. Prokhorov.
\newblock Fano varieties.
\newblock In {\em Algebraic geometry, {V}}, volume~47 of {\em Encyclopaedia
  Math. Sci.}, pages 1--247. Springer, Berlin, 1999.

\bibitem[Jan88]{JannsenMA}
Uwe Jannsen.
\newblock Continuous \'{e}tale cohomology.
\newblock {\em Math. Ann.}, 280(2):207--245, 1988.

\bibitem[Jan90]{JannsenBook}
Uwe Jannsen.
\newblock {\em Mixed motives and algebraic {$K$}-theory}, volume 1400 of {\em
  Lecture Notes in Mathematics}.
\newblock Springer-Verlag, Berlin, 1990.
\newblock With appendices by S. Bloch and C. Schoen.

\bibitem[Kol96]{KollarBook}
J\'{a}nos Koll\'{a}r.
\newblock {\em Rational curves on algebraic varieties}, volume~32 of {\em
  Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge}.
\newblock Springer-Verlag, Berlin, 1996.

\bibitem[Kol08]{KollarLooking}
J\'{a}nos Koll\'{a}r.
\newblock Looking for rational curves on cubic hypersurfaces.
\newblock In {\em Higher-dimensional geometry over finite fields}, volume~16 of
  {\em NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur.}, pages 92--122. IOS,
  Amsterdam, 2008.
\newblock Notes by Ulrich Derenthal.

\bibitem[Kuz16]{KuzSurvey}
Alexander Kuznetsov.
\newblock Derived categories view on rationality problems.
\newblock In {\em Rationality problems in algebraic geometry}, volume 2172 of
  {\em Lecture Notes in Math.}, pages 67--104. Springer, Cham, 2016.

\bibitem[Kuz19]{KuzLetter}
Alexander Kuznetsov.
\newblock Rationality of geometrically rational threefolds, 2019.
\newblock April 19 letter to Olivier Wittenberg.

\bibitem[Lau01]{SerreLauter}
Kristin Lauter.
\newblock Geometric methods for improving the upper bounds on the number of
  rational points on algebraic curves over finite fields.
\newblock {\em J. Algebraic Geom.}, 10(1):19--36, 2001.
\newblock With an appendix in French by J.-P. Serre.

\bibitem[Man68]{ManinMotive}
Yu.~I. Manin.
\newblock Correspondences, motifs and monoidal transformations.
\newblock {\em Mat. Sb. (N.S.)}, 77 (119):475--507, 1968.

\bibitem[Ser60]{SerreMorphism}
Jean-Pierre Serre.
\newblock Morphismes universels et vari\'et\'e d'{A}lbanese.
\newblock In {\em S\'{e}minaire {C}. {C}hevalley, 3i\`eme ann\'{e}e: 1958/59.
  {V}ari\'{e}t\'{e}s de {P}icard}, pages ii+182. \'{E}cole Normale
  Sup\'{e}rieure, Paris, 1960.

\bibitem[TZ14]{TianZong}
Zhiyu Tian and Hong~R. Zong.
\newblock One-cycles on rationally connected varieties.
\newblock {\em Compos. Math.}, 150(3):396--408, 2014.

\bibitem[Voi06]{VoisinIHC}
Claire Voisin.
\newblock On integral {H}odge classes on uniruled or {C}alabi-{Y}au threefolds.
\newblock In {\em Moduli spaces and arithmetic geometry}, volume~45 of {\em
  Adv. Stud. Pure Math.}, pages 43--73. Math. Soc. Japan, Tokyo, 2006.

\bibitem[Wan18]{wang}
Xiaoheng Wang.
\newblock Maximal linear spaces contained in the base loci of pencils of
  quadrics.
\newblock {\em Algebr. Geom.}, 5(3):359--397, 2018.

\bibitem[Wit19a]{WitLetter1}
Olivier Wittenberg.
\newblock April 16 letter to {J}.~{L}.~{C}olliot-{T}h\'el\`ene, 2019.

\bibitem[Wit19b]{WitLetter2}
Olivier Wittenberg.
\newblock April 17 letter to {J}.~{L}.~{C}olliot-{T}h\'el\`ene, 2019.

\end{thebibliography}
