Geodesic
Rationality Problem for Classifying Spaces of Spinor Groups
Informatics and Automation, Algebra, number theory, and algebraic geometry, Tome 307 (2019), pp. 132-141.

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We study stable rationality and retract rationality properties of the classifying spaces of split spinor groups $\mathbf {Spin}_n$ over a field $F$ of characteristic different from $2$. 
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     title = {Rationality {Problem} for {Classifying} {Spaces} of {Spinor} {Groups}},
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     url = {http://geodesic.mathdoc.fr/item/TRSPY_2019_307_a5/}
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Alexander S. Merkurjev. Rationality Problem for Classifying Spaces of Spinor Groups. Informatics and Automation, Algebra, number theory, and algebraic geometry, Tome 307 (2019), pp. 132-141. http://geodesic.mathdoc.fr/item/TRSPY_2019_307_a5/

[1] F. A. Bogomolov, “The stable rationality of quotient spaces for simply connected groups”, Math. USSR, Sb., 58:1 (1987), 1–14 | DOI | MR | Zbl | Zbl

[2] Bogomolov F., Böhning C., “Isoclinism and stable cohomology of wreath products”, Birational geometry, rational curves, and arithmetic, Simons Symp., Springer, New York, 2013, 57–76 | MR | Zbl

[3] Borel A., Springer T.A., “Rationality properties of linear algebraic groups. II”, Tôhoku Math. J. Ser. 2, 20 (1968), 443–497 | DOI | MR | Zbl

[4] Colliot-Thélène J.-L., Sansuc J.-J., “The rationality problem for fields of invariants under linear algebraic groups (with special regards to the Brauer group)”, Algebraic groups and homogeneous spaces, Proc. Int. Colloq. (Mumbai, 2004), Stud. Math. Tata Inst. Fundam. Res., 19, Narosa Publ. House, New Delhi, 2007, 113–186 | MR | Zbl

[5] Elman R., Karpenko N., Merkurjev A., The algebraic and geometric theory of quadratic forms, Colloq. Publ., 56, Amer. Math. Soc., Providence, RI, 2008 | DOI | MR | Zbl

[6] Garibaldi S., Merkurjev A., Serre J.-P., Cohomological invariants in Galois cohomology, Univ. Lect. Ser., 28, Amer. Math. Soc., Providence, RI, 2003 | DOI | MR | Zbl

[7] Grothendieck A., “Le groupe de Brauer. I: Algèbres d'Azumaya et interprétations diverses”, Dix exposés sur la cohomologie des schémas, Adv. Stud. Pure Math., 3, North-Holland, Amsterdam, 1968, 46–66 | MR

[8] Knus M.-A., Merkurjev A., Rost M., Tignol J.-P., The book of involutions, With a preface in French by J. Tits, Colloq. Publ., 44, Amer. Math. Soc., Providence, RI, 1998 | DOI | MR | Zbl

[9] V. È. Kordonskii, “Stable rationality of the group $\mathrm {Spin}_{10}$”, Russ. Math. Surv., 55:1 (2000), 178–179 | DOI | DOI | MR

[10] Lam T.Y., Introduction to quadratic forms over fields, Grad. Stud. Math., 67, Amer. Math. Soc., Providence, RI, 2005 | MR | Zbl

[11] Merkurjev A.S., “Invariants of algebraic groups and retract rationality of classifying spaces”, Algebraic groups: Structure and actions, Proc. Symp. Pure Math., 94, Amer. Math. Soc., Providence, RI, 2017, 277–294 | DOI | MR | Zbl

[12] Merkurjev A.S., “Versal torsors and retracts”, Transform. Groups, 2019 | DOI | MR

[13] Saltman D., “Norm polynomials and algebras”, J. Algebra, 62:2 (1980), 333–345 | DOI | MR | Zbl

[14] Thomason R.W., “Comparison of equivariant algebraic and topological $K$-theory”, Duke Math. J., 53:3 (1986), 795–825 | DOI | MR | Zbl