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\bibitem[A'C75]{AC}
Norbert A'Campo.
\newblock La fonction z\^eta d'une monodromie.
\newblock {\em Comment. Math. Helv.}, 50:233--248, 1975.

\bibitem[Add17]{Adding}
Nicolas Addington.
\newblock The {B}rauer group is not a derived invariant.
\newblock In {\em Brauer groups and obstruction problems: moduli spaces and
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\bibitem[ADPZ17]{ADPZ}
Kenneth Ascher, Krishna Dasaratha, Alexander Perry, and Rong Zhou.
\newblock Derived equivalences and rational points of twisted {$K3$} surfaces.
\newblock In {\em Brauer groups and obstruction problems: moduli spaces and
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  Birkh\"auser/Springer, New York, 2017.

\bibitem[AKW14]{AKW}
Benjamin Antieau, Daniel Krashen, and Matthew Ward.
\newblock Derived categories of torsors for abelian schemes, 2014.
\newblock arXiv:1409.2580.

\bibitem[Art74]{Artin}
Michael Artin.
\newblock Algebraic construction of {B}rieskorn's resolutions.
\newblock {\em J. Algebra}, 29:330--348, 1974.

\bibitem[Art77]{Artin2}
Michael Artin.
\newblock Coverings of the rational double points in characteristic {$p$}.
\newblock In {\em Complex analysis and algebraic geometry}, pages 11--22.
  Iwanami Shoten, Tokyo, 1977.

\bibitem[Ati57]{Atiyah}
Michael~F. Atiyah.
\newblock Vector bundles over an elliptic curve.
\newblock {\em Proc. London Math. Soc. (3)}, 7:414--452, 1957.

\bibitem[BM02]{BrMa}
Tom Bridgeland and Antony Maciocia.
\newblock Fourier-{M}ukai transforms for {$K3$} and elliptic fibrations.
\newblock {\em J. Algebraic Geom.}, 11(4):629--657, 2002.

\bibitem[BM14]{BM2}
Arend Bayer and Emanuele Macr{\`{\i}}.
\newblock M{MP} for moduli of sheaves on {K}3s via wall-crossing: nef and
  movable cones, {L}agrangian fibrations.
\newblock {\em Invent. Math.}, 198(3):505--590, 2014.

\bibitem[BMT14]{BM1}
Arend Bayer, Emanuele Macr{\`{\i}}, and Yukinobu Toda.
\newblock Bridgeland stability conditions on threefolds {I}:
  {B}ogomolov-{G}ieseker type inequalities.
\newblock {\em J. Algebraic Geom.}, 23(1):117--163, 2014.
\newblock arXiv:1203.4613.

\bibitem[Bri71]{Bries}
E.~Brieskorn.
\newblock Singular elements of semi-simple algebraic groups.
\newblock In {\em Actes du {C}ongr\`es {I}nternational des {M}ath\'ematiciens
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\bibitem[Bri98]{BrCrelle}
Tom Bridgeland.
\newblock Fourier-{M}ukai transforms for elliptic surfaces.
\newblock {\em J. Reine Angew. Math.}, 498:115--133, 1998.

\bibitem[Bri07]{Br1}
Tom Bridgeland.
\newblock Stability conditions on triangulated categories.
\newblock {\em Ann. of Math. (2)}, 166(2):317--345, 2007.

\bibitem[BV04]{BV}
Arnaud Beauville and Claire Voisin.
\newblock On the {C}how ring of a {$K3$} surface.
\newblock {\em J. Algebraic Geom.}, 13(3):417--426, 2004.

\bibitem[C{\u{a}}l00]{CalThe}
Andrei~Horia C{\u{a}}ld{\u{a}}raru.
\newblock {\em Derived categories of twisted sheaves on {C}alabi-{Y}au
  manifolds}.
\newblock ProQuest LLC, Ann Arbor, MI, 2000.
\newblock Thesis (Ph.D.)--Cornell University.

\bibitem[CEZGT14]{CEGT}
Eduardo Cattani, Fouad El~Zein, Phillip~A. Griffiths, and L{\^e}~D{\~u}ng
  Tr{\'a}ng, editors.
\newblock {\em Hodge theory}, volume~49 of {\em Mathematical Notes}.
\newblock Princeton University Press, Princeton, NJ, 2014.

\bibitem[Fri83]{Friedman}
Robert Friedman.
\newblock Base change, automorphisms, and stable reduction for type {${\rm
  III}\,K3$} surfaces.
\newblock In {\em The birational geometry of degenerations ({C}ambridge,
  {M}ass., 1981)}, volume~29 of {\em Progr. Math.}, pages 277--298.
  Birkh\"auser Boston, Mass., 1983.

\bibitem[Fri84]{FriedAnnals}
Robert Friedman.
\newblock A new proof of the global {T}orelli theorem for {$K3$} surfaces.
\newblock {\em Ann. of Math. (2)}, 120(2):237--269, 1984.

\bibitem[FS85]{FriSca}
Robert Friedman and Francesco Scattone.
\newblock Type {${\rm III}$} degenerations of {$K3$} surfaces.
\newblock {\em Invent. Math.}, 83(1):1--39, 1985.

\bibitem[HLOY04a]{HLOY3}
Shinobu Hosono, Bong~H. Lian, Keiji Oguiso, and Shing-Tung Yau.
\newblock Autoequivalences of derived category of a {$K3$} surface and
  monodromy transformations.
\newblock {\em J. Algebraic Geom.}, 13(3):513--545, 2004.

\bibitem[HLOY04b]{HLOY}
Shinobu Hosono, Bong~H. Lian, Keiji Oguiso, and Shing-Tung Yau.
\newblock Fourier-{M}ukai number of a {K}3 surface.
\newblock In {\em Algebraic structures and moduli spaces}, volume~38 of {\em
  CRM Proc. Lecture Notes}, pages 177--192. Amer. Math. Soc., Providence, RI,
  2004.

\bibitem[Hon15]{Honigs}
Katrina Honigs.
\newblock Derived equivalent surfaces and abelian varieties, and their zeta
  functions.
\newblock {\em Proc. Amer. Math. Soc.}, 143(10):4161--4166, 2015.

\bibitem[HS06]{HuSt}
Daniel Huybrechts and Paolo Stellari.
\newblock Proof of {C}\u ald\u araru's conjecture. {A}ppendix: ``{M}oduli
  spaces of twisted sheaves on a projective variety'' [in {\it {m}oduli spaces
  and arithmetic geometry}, 1--30, {M}ath. {S}oc. {J}apan, {T}okyo, 2006; ] by
  {K}. {Y}oshioka.
\newblock In {\em Moduli spaces and arithmetic geometry}, volume~45 of {\em
  Adv. Stud. Pure Math.}, pages 31--42. Math. Soc. Japan, Tokyo, 2006.

\bibitem[Huy08]{HuyJAG08}
Daniel Huybrechts.
\newblock Derived and abelian equivalence of {$K3$} surfaces.
\newblock {\em J. Algebraic Geom.}, 17(2):375--400, 2008.

\bibitem[Huy10]{HuyEMS}
Daniel Huybrechts.
\newblock Chow groups of {K}3 surfaces and spherical objects.
\newblock {\em J. Eur. Math. Soc. (JEMS)}, 12(6):1533--1551, 2010.

\bibitem[Huy12a]{HuyMSRI}
Daniel Huybrechts.
\newblock Chow groups and derived categories of {K}3 surfaces.
\newblock In {\em Current developments in algebraic geometry}, volume~59 of
  {\em Math. Sci. Res. Inst. Publ.}, pages 177--195. Cambridge Univ. Press,
  Cambridge, 2012.

\bibitem[Huy12b]{HuySur}
Daniel Huybrechts.
\newblock A global {T}orelli theorem for hyperk\"ahler manifolds [after {M}.
  {V}erbitsky].
\newblock {\em Ast\'erisque}, (348):Exp. No. 1040, x, 375--403, 2012.
\newblock S{\'e}minaire Bourbaki: Vol. 2010/2011. Expos{\'e}s 1027--1042.

\bibitem[Huy16]{HuyK3}
Daniel Huybrechts.
\newblock {\em Lectures on {$K3$} surfaces}, volume 158 of {\em Cambridge
  Studies in Advanced Mathematics}.
\newblock Cambridge University Press, 2016.

\bibitem[HVA13]{HVA2}
Brendan Hassett and Anthony V{\'a}rilly-Alvarado.
\newblock Failure of the {H}asse principle on general {$K3$} surfaces.
\newblock {\em J. Inst. Math. Jussieu}, 12(4):853--877, 2013.

\bibitem[HVAV11]{HVA1}
Brendan Hassett, Anthony V{\'a}rilly-Alvarado, and Patrick Varilly.
\newblock Transcendental obstructions to weak approximation on general {K}3
  surfaces.
\newblock {\em Adv. Math.}, 228(3):1377--1404, 2011.

\bibitem[KKMSD73]{KKMS}
George Kempf, Finn~Faye Knudsen, D.~Mumford, and Bernard Saint-Donat.
\newblock {\em Toroidal embeddings. {I}}.
\newblock Lecture Notes in Mathematics, Vol. 339. Springer-Verlag, Berlin,
  1973.

\bibitem[KM92]{KaMo}
Sheldon Katz and David~R. Morrison.
\newblock Gorenstein threefold singularities with small resolutions via
  invariant theory for {W}eyl groups.
\newblock {\em J. Algebraic Geom.}, 1(3):449--530, 1992.

\bibitem[KM98]{KM}
J{\'a}nos Koll{\'a}r and Shigefumi Mori.
\newblock {\em Birational geometry of algebraic varieties}, volume 134 of {\em
  Cambridge Tracts in Mathematics}.
\newblock Cambridge University Press, Cambridge, 1998.
\newblock With the collaboration of C. H. Clemens and A. Corti, Translated from
  the 1998 Japanese original.

\bibitem[Kul77]{Kulikov}
Viktor~S. Kulikov.
\newblock Degenerations of {$K3$} surfaces and {E}nriques surfaces.
\newblock {\em Izv. Akad. Nauk SSSR Ser. Mat.}, 41(5):1008--1042, 1199, 1977.

\bibitem[Kul89]{Kuleshov}
Sergej~A. Kuleshov.
\newblock A theorem on the existence of exceptional bundles on surfaces of type
  {$K3$}.
\newblock {\em Izv. Akad. Nauk SSSR Ser. Mat.}, 53(2):363--378, 1989.

\bibitem[Kul90]{Kuleshov2}
Sergej~A. Kuleshov.
\newblock Exceptional bundles on {$K3$} surfaces.
\newblock In {\em Helices and vector bundles}, volume 148 of {\em London Math.
  Soc. Lecture Note Ser.}, pages 105--114. Cambridge Univ. Press, Cambridge,
  1990.

\bibitem[Lan73]{Landman}
Alan Landman.
\newblock On the {P}icard-{L}efschetz transformation for algebraic manifolds
  acquiring general singularities.
\newblock {\em Trans. Amer. Math. Soc.}, 181:89--126, 1973.

\bibitem[LO15]{LO}
Max Lieblich and Martin Olsson.
\newblock Fourier-{M}ukai partners of {K}3 surfaces in positive characteristic.
\newblock {\em Ann. Sci. \'Ec. Norm. Sup\'er. (4)}, 48(5):1001--1033, 2015.

\bibitem[Mar10]{Markman2010}
Eyal Markman.
\newblock Integral constraints on the monodromy group of the hyper{K}\"ahler
  resolution of a symmetric product of a {$K3$} surface.
\newblock {\em Internat. J. Math.}, 21(2):169--223, 2010.

\bibitem[Mat15]{Mat}
Yuya Matsumoto.
\newblock Good reduction criterion for {K}3 surfaces.
\newblock {\em Math. Z.}, 279(1-2):241--266, 2015.

\bibitem[ML14]{LieMat}
Yuya Matsumoto and Christian Liedtke.
\newblock Good reduction of {$K3$} surfaces, 2014.
\newblock arXiv:1411.4797.

\bibitem[MM83]{MiMo}
Rick Miranda and David~R. Morrison.
\newblock The minus one theorem.
\newblock In {\em The birational geometry of degenerations ({C}ambridge,
  {M}ass., 1981)}, volume~29 of {\em Progr. Math.}, pages 173--259.
  Birkh\"auser Boston, Boston, MA, 1983.

\bibitem[Mor84]{Morrison}
David~R. Morrison.
\newblock The {C}lemens-{S}chmid exact sequence and applications.
\newblock In {\em Topics in transcendental algebraic geometry ({P}rinceton,
  {N}.{J}., 1981/1982)}, volume 106 of {\em Ann. of Math. Stud.}, pages
  101--119. Princeton Univ. Press, Princeton, NJ, 1984.

\bibitem[MSTVA17]{MSTVA}
Kelly McKinnie, Justin Sawon, Sho Tanimoto, and Anthony V\'arilly-Alvarado.
\newblock Brauer groups on {K}3 surfaces and arithmetic applications.
\newblock In {\em Brauer groups and obstruction problems: moduli spaces and
  arithmetic}, volume 320 of {\em Progr. Math.}, pages 177--218.
  Birkh\"auser/Springer, New York, 2017.

\bibitem[Muk87]{Mukai}
Shigeru Mukai.
\newblock On the moduli space of bundles on {$K3$} surfaces. {I}.
\newblock In {\em Vector bundles on algebraic varieties ({B}ombay, 1984)},
  volume~11 of {\em Tata Inst. Fund. Res. Stud. Math.}, pages 341--413. Tata
  Inst. Fund. Res., Bombay, 1987.

\bibitem[Nic11]{Nicaise}
Johannes Nicaise.
\newblock A trace formula for varieties over a discretely valued field.
\newblock {\em J. Reine Angew. Math.}, 650:193--238, 2011.

\bibitem[Nik79]{Nik79}
Viacheslav~V. Nikulin.
\newblock Integer symmetric bilinear forms and some of their geometric
  applications.
\newblock {\em Izv. Akad. Nauk SSSR Ser. Mat.}, 43(1):111--177, 238, 1979.

\bibitem[Nik08]{Nik08}
Viacheslav~V. Nikulin.
\newblock On connected components of moduli of real polarized {$K3$} surfaces.
\newblock {\em Izv. Ross. Akad. Nauk Ser. Mat.}, 72(1):99--122, 2008.

\bibitem[Ogu02]{Oguiso}
Keiji Oguiso.
\newblock K3 surfaces via almost-primes.
\newblock {\em Math. Res. Lett.}, 9(1):47--63, 2002.

\bibitem[Orl97]{Orlov}
Dmitri~O. Orlov.
\newblock Equivalences of derived categories and {$K3$} surfaces.
\newblock {\em J. Math. Sci. (New York)}, 84(5):1361--1381, 1997.
\newblock Algebraic geometry, 7.

\bibitem[PP81]{PerPin}
Ulf Persson and Henry Pinkham.
\newblock Degeneration of surfaces with trivial canonical bundle.
\newblock {\em Ann. of Math. (2)}, 113(1):45--66, 1981.

\bibitem[P{\v{S}}{\v{S}}71]{PSSh}
I.~I. Pjatecki{\u\i}-{\v{S}}apiro and I.~R. {\v{S}}afarevi{\v{c}}.
\newblock Torelli's theorem for algebraic surfaces of type {${\rm K}3$}.
\newblock {\em Izv. Akad. Nauk SSSR Ser. Mat.}, 35:530--572, 1971.

\bibitem[Rei83]{Reid83}
Miles Reid.
\newblock Minimal models of canonical {$3$}-folds.
\newblock In {\em Algebraic varieties and analytic varieties ({T}okyo, 1981)},
  volume~1 of {\em Adv. Stud. Pure Math.}, pages 131--180. North-Holland,
  Amsterdam, 1983.

\bibitem[SB83]{ShB}
Nicholas~I. Shepherd-Barron.
\newblock Extending polarizations on families of {$K3$} surfaces.
\newblock In {\em The birational geometry of degenerations ({C}ambridge,
  {M}ass., 1981)}, volume~29 of {\em Progr. Math.}, pages 135--171.
  Birkh\"auser Boston, Mass., 1983.

\bibitem[SD74]{SD}
B.~Saint-Donat.
\newblock Projective models of {$K3$} surfaces.
\newblock {\em Amer. J. Math.}, 96:602--639, 1974.

\bibitem[Sos10]{Sosna}
Pawel Sosna.
\newblock Derived equivalent conjugate {$K3$} surfaces.
\newblock {\em Bull. Lond. Math. Soc.}, 42(6):1065--1072, 2010.

\bibitem[Ste04]{Stellari04}
Paolo Stellari.
\newblock Some remarks about the {FM}-partners of {$K3$} surfaces with {P}icard
  numbers 1 and 2.
\newblock {\em Geom. Dedicata}, 108:1--13, 2004.

\bibitem[Ver13]{Verb}
Misha Verbitsky.
\newblock Mapping class group and a global {T}orelli theorem for hyperk\"ahler
  manifolds.
\newblock {\em Duke Math. J.}, 162(15):2929--2986, 2013.
\newblock Appendix A by Eyal Markman.

\end{thebibliography}