\begin{thebibliography}{CTP16b}

\bibitem[Bea15]{Beau-AG}
Arnaud Beauville.
\newblock A very general quartic double fourfold or fivefold is not stably
  rational.
\newblock {\em Algebr. Geom.}, 2(4):508--513, 2015.

\bibitem[Bea16a]{Beau-AG-E}
Arnaud Beauville.
\newblock Erratum: A very general quartic double fourfold or fivefold is not
  stably rational (algebraic geometry 2, no. 4 (2015), 508-513).
\newblock {\em Algebr. Geom.}, 3(1):137--137, 2016.

\bibitem[Bea16b]{beau-6}
Arnaud Beauville.
\newblock A very general sextic double solid is not stably rational.
\newblock {\em Bull. Lond. Math. Soc.}, 48(2):321--324, 2016.
\newblock {\tt arXiv:1411.7484}.

\bibitem[CTP16a]{ct-pir-cyclic}
Jean-Louis Colliot-Th\'el\`ene and Alena Pirutka.
\newblock Cyclic covers that are not stably rational.
\newblock {\em Izvestiya RAN, Ser. Math.}, 80(4), 2016.
\newblock {\tt arXiv:1506.0042v2}.

\bibitem[CTP16b]{ct-pirutka}
Jean-Louis Colliot-Th\'el\`ene and Alena Pirutka.
\newblock Hypersurfaces quartiques de dimension 3 : non rationalit\'e stable.
\newblock {\em Ann. Sci. ENS}, 49(2):735--801, 2016.

\bibitem[GM88]{GM}
Mark Goresky and Robert MacPherson.
\newblock {\em Stratified {M}orse theory}, volume~14 of {\em Ergebnisse der
  Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related
  Areas (3)]}.
\newblock Springer-Verlag, Berlin, 1988.

\bibitem[HPT16]{HPT}
Brendan Hassett, Alena Pirutka, and Yuri Tschinkel.
\newblock Stable rationality quadric surface bundles over surfaces, 2016.
\newblock {\tt arXiv:1603.09262}.

\bibitem[Oka16]{okada}
Takuzo Okada.
\newblock Stable rationality of cyclic covers of projective spaces, 2016.
\newblock {\tt arXiv:1604.08417}.

\bibitem[Pir16]{pirutka-survol}
Alena Pirutka.
\newblock Varieties that are not stably rational, zero-cycles and unramified
  cohomology, 2016.
\newblock {\tt arXiv:1603.09261}.

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

\bibitem[Voi15a]{voisin-stable}
Claire Voisin.
\newblock ({S}table) rationality is not deformation invariant, 2015.
\newblock {\tt arXiv:1511.03591}.

\bibitem[Voi15b]{Voisin}
Claire Voisin.
\newblock Unirational threefolds with no universal codimension {$2$} cycle.
\newblock {\em Invent. Math.}, 201(1):207--237, 2015.

\end{thebibliography}