\begin{thebibliography}{MSTVA17}

\bibitem[BW19]{BW}
Olivier Benoist and Olivier Wittenberg.
\newblock Intermediate {J}acobians and rationality over arbitrary fields, 2019.
\newblock \texttt{arXiv:1909.12668}.

\bibitem[CTP16]{CTP}
Jean-Louis Colliot-Th\'{e}l\`ene and Alena Pirutka.
\newblock Hypersurfaces quartiques de dimension 3: non-rationalit\'{e} stable.
\newblock {\em Ann. Sci. \'{E}c. Norm. Sup\'{e}r. (4)}, 49(2):371--397, 2016.

\bibitem[HKT16]{HTK}
Brendan Hassett, Andrew Kresch, and Yuri Tschinkel.
\newblock Stable rationality and conic bundles.
\newblock {\em Math. Ann.}, 365(3-4):1201--1217, 2016.

\bibitem[HPT18]{HPTActa}
Brendan Hassett, Alena Pirutka, and Yuri Tschinkel.
\newblock Stable rationality of quadric surface bundles over surfaces.
\newblock {\em Acta Math.}, 220(2):341--365, 2018.

\bibitem[HT19a]{HTcycle}
Brendan Hassett and Yuri Tschinkel.
\newblock Cycle class maps and birational invariants, 2019.
\newblock \texttt{arXiv:1908.00406}.

\bibitem[HT19b]{HT2quad}
Brendan Hassett and Yuri Tschinkel.
\newblock Rationality of complete intersections of two quadrics, 2019.
\newblock \texttt{arXiv:1903.08979}.

\bibitem[IM07]{IlMa}
Atanas Iliev and Laurent Manivel.
\newblock Prime {F}ano threefolds and integrable systems.
\newblock {\em Math. Ann.}, 339(4):937--955, 2007.

\bibitem[IP99]{IskPro}
V.~A. Iskovskikh and Yu.~G. Prokhorov.
\newblock {\em Algebraic geometry. {V}: {F}ano varieties}, volume~47 of {\em
  Encyclopaedia of Mathematical Sciences}.
\newblock Springer-Verlag, Berlin, 1999.
\newblock A.N. Parshin and I.R. Shafarevich eds.

\bibitem[KP19]{KP}
Alexander~G. Kuznetsov and Yuri~G. Prokhorov.
\newblock Rationality of {F}ano threefolds over non-closed fields, 2019.
\newblock {\tt arXiv:1911.08949}.

\bibitem[KPS18]{KuzPro}
Alexander~G. Kuznetsov, Yuri~G. Prokhorov, and Constantin~A. Shramov.
\newblock Hilbert schemes of lines and conics and automorphism groups of {F}ano
  threefolds.
\newblock {\em Jpn. J. Math.}, 13(1):109--185, 2018.

\bibitem[KR13]{KR}
Micha\l{\,} Kapusta and Kristian Ranestad.
\newblock Vector bundles on {F}ano varieties of genus ten.
\newblock {\em Math. Ann.}, 356(2):439--467, 2013.

\bibitem[KST89]{KST}
B.~\`E. Kunyavski\u{\i}, A.~N. Skorobogatov, and M.~A. Tsfasman.
\newblock del {P}ezzo surfaces of degree four.
\newblock {\em M\'{e}m. Soc. Math. France (N.S.)}, (37):113, 1989.

\bibitem[KT19]{KTspecialize}
Maxim Kontsevich and Yuri Tschinkel.
\newblock Specialization of birational types.
\newblock {\em Invent. Math.}, 217(2):415--432, 2019.

\bibitem[Man66]{Manin66}
Ju.~I. Manin.
\newblock Rational surfaces over perfect fields.
\newblock {\em Inst. Hautes \'{E}tudes Sci. Publ. Math.}, (30):55--113, 1966.

\bibitem[Man93]{Manin3fold}
Yu.~I. Manin.
\newblock Notes on the arithmetic of {F}ano threefolds.
\newblock {\em Compositio Math.}, 85(1):37--55, 1993.

\bibitem[Mar06]{Mark}
Dimitri Markushevich.
\newblock Rational {L}agrangian fibrations on punctual {H}ilbert schemes of
  {$K3$} surfaces.
\newblock {\em Manuscripta Math.}, 120(2):131--150, 2006.

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

\bibitem[Muk88]{Mukai}
Shigeru Mukai.
\newblock Curves, {$K3$} surfaces and {F}ano {$3$}-folds of genus {$\leq 10$}.
\newblock In {\em Algebraic geometry and commutative algebra, {V}ol. {I}},
  pages 357--377. Kinokuniya, Tokyo, 1988.

\bibitem[NS19]{NS}
Johannes Nicaise and Evgeny Shinder.
\newblock The motivic nearby fiber and degeneration of stable rationality.
\newblock {\em Invent. Math.}, 217(2):377--413, 2019.

\bibitem[Pro90]{ProkhorovAut}
Yu.~G. Prokhorov.
\newblock Automorphism groups of {F}ano {$3$}-folds.
\newblock {\em Uspekhi Mat. Nauk}, 45(3(273)):195--196, 1990.

\bibitem[RS19]{RS}
Francesco Russo and Giovanni Staglian\`o.
\newblock Congruences of 5-secant conics and the rationality of some admissible
  cubic fourfolds.
\newblock {\em Duke Math. J.}, 168(5):849--865, 2019.

\bibitem[Saw07]{Sawon}
Justin Sawon.
\newblock Lagrangian fibrations on {H}ilbert schemes of points on {$K3$}
  surfaces.
\newblock {\em J. Algebraic Geom.}, 16(3):477--497, 2007.

\bibitem[Sch19]{Schreieder}
Stefan Schreieder.
\newblock Stably irrational hypersurfaces of small slopes.
\newblock {\em J. Amer. Math. Soc.}, 32(4):1171--1199, 2019.

\bibitem[Tak89]{Takeuchi}
Kiyohiko Takeuchi.
\newblock Some birational maps of {F}ano {$3$}-folds.
\newblock {\em Compositio Math.}, 71(3):265--283, 1989.

\bibitem[Tot16]{Totaro}
Burt Totaro.
\newblock Hypersurfaces that are not stably rational.
\newblock {\em J. Amer. Math. Soc.}, 29(3):883--891, 2016.

\bibitem[Ver18]{VerraSlide}
Alessandro Verra.
\newblock Coble cubic, genus 10 {F}ano threefolds and the theta map, 2018.
\newblock Lecture at the `Differential, Algebraic and Topological Methods in
  Complex Algebraic Geometry' conference held at Cetraro, Italy.

\bibitem[Voi15]{VoisinInv}
Claire Voisin.
\newblock Unirational threefolds with no universal codimension {$2$} cycle.
\newblock {\em Invent. Math.}, 201(1):207--237, 2015.

\end{thebibliography}
