Geodesic
Rationality Problem for Classifying Spaces of Spinor Groups
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebra, number theory, and algebraic geometry, Tome 307 (2019), pp. 132-141.

Voir la notice de l'article provenant de la source Math-Net.Ru

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 $2$. 
@article{TM_2019_307_a5,
     author = {Alexander S. Merkurjev},
     title = {Rationality {Problem} for {Classifying} {Spaces} of {Spinor} {Groups}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {132--141},
     publisher = {mathdoc},
     volume = {307},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2019_307_a5/}
}
TY  - JOUR
AU  - Alexander S. Merkurjev
TI  - Rationality Problem for Classifying Spaces of Spinor Groups
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2019
SP  - 132
EP  - 141
VL  - 307
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2019_307_a5/
LA  - ru
ID  - TM_2019_307_a5
ER  - 
%0 Journal Article
%A Alexander S. Merkurjev
%T Rationality Problem for Classifying Spaces of Spinor Groups
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2019
%P 132-141
%V 307
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2019_307_a5/
%G ru
%F TM_2019_307_a5
Alexander S. Merkurjev. Rationality Problem for Classifying Spaces of Spinor Groups. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebra, number theory, and algebraic geometry, Tome 307 (2019), pp. 132-141. http://geodesic.mathdoc.fr/item/TM_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