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VERSAL TORSORS AND RETRACTS

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Abstract

Let G be an algebraic group over F and p a prime integer. We introduce the notion of a p-retract rational variety and prove that if Y → X is a p-versal G-torsor, then BG is a stable p-retract of X. It follows that the classifying space BG is p-retract rational if and only if there is a p-versal G-torsor Y → X with X a rational variety, that is, all G-torsors over infinite fields are rationally parameterized. In particular, for such groups G the unramified Galois cohomology group \( {H}_{\mathrm{nr}}^n \) (F(BG), ℚp/ℤp(j)) coincides with Hn(F, ℚp/ℤp(j)).

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  1. Department of Mathematics, University of California, Los Angeles, CA, 90095-1555, USA

    A. S. MERKURJEV

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A. S. Merkurjev Supported by NSF grant DMS #1801530.

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MERKURJEV, A.S. VERSAL TORSORS AND RETRACTS. Transformation Groups 25, 843–858 (2020). https://doi.org/10.1007/s00031-019-09521-y

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