Abstract.
Using a cohomological obstruction, we construct examples of absolutely simple adjoint classical groups of type 2A n with n≡3mod4, C n or 1D n with n≡0mod4, which are not R-trivial hence not stably rational.
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Berhuy, G., Monsurrò, M., Tignol, J.-P.: The discriminant of a symplectic involution. Pacific J. of Math. 209, 201–218 (2003)
Colliot-Thélène, J.-L., Sansuc, J.-J.: La R-équivalence sur les tores. Ann. scient. Éc. Norm. Sup., 4e série. 10, 175–230 (1997)
Gille, P.: Examples of non-rational varieties of adjoint groups. J. Algebra. 193, 728–747 (1997)
Knus, M.-A., Merkurjev, A.S., Rost, M., Tignol, J.-P.: The Book of Involutions. (Amer. Math. Soc. Coll. Pub. 44, AMS, Providence, RI, 1998)
Lewis, D.W.: A note on trace forms and involutions of the first kind. Exposition. Math. 15, 265–272 (1997)
Manin, Y.: Cubic forms. (North-Holland, Amsterdam, 1974)
Merkurjev, A.: R-equivalence and rationality problem for semisimple adjoint classical algebraic groups. Pub. Math. IHES 46, 189–213 (1996)
Merkurjev, A., Parimala, R., Tignol, J.-P.: Invariants of quasi-trivial tori and the Rost invariant. Algebra i Analiz 14, 110–151 (2002); transl. in St. Petersburg Math. J. 14, 791–821 (2003)
Merkurjev, A., Tignol, J.-P.: The multipliers of similitudes and the Brauer group of homogeneous varieties. J. reine angew. Math. 461, 13–47 (1995)
Quéguiner, A.: Cohomological invariants of algebras with involution. J. Algebra 194, 299–330 (1997)
Voskresenskii, V.E., Klyachko, A.A.: Toroidal Fano varieties and root system. Math. USSR Izvestija 24, 221–244 (1985)
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Mathematics Subject Classification (2000): 11E57, 20G15
in final form: 13 June 2003
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Berhuy, G., Monsurrò, M. & Tignol, JP. Cohomological invariants and R-triviality of adjoint classical groups. Math. Z. 248, 313–323 (2004). https://doi.org/10.1007/s00209-003-0611-2
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DOI: https://doi.org/10.1007/s00209-003-0611-2