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arXiv · 1109.2802

Prime-to-p étale covers of algebraic groups

Michel Brion·Tamás Szamuely
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Abstract

Let G be a connected algebraic group over an algebraically closed field of characteristic p (possibly 0), and X a variety on which G acts transitively with connected stabilizers. We show that any étale Galois cover of X of degree prime to p is also homogeneous, and that the maximal prime-to-p quotient of the étale fundamental group of X is commutative. We moreover obtain an explicit bound for the number of topological generators of the said quotient. When G is commutative, we also obtain a description of the prime-to-p torsion in the Brauer group of G.

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Michel Brion, Tamás Szamuely. 2012-09-28. Prime-to-p étale covers of algebraic groups. https://arxiv.org/abs/1109.2802

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