Galois cohomology revisited

2017/12/20 by Nikolaev, Igor V.
#11G35 #14A22 #46L85 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1712.07516

Abstract

We recast the Galois cohomology of the variety V over a number field k in terms of the K-theory of a C^*-algebra \mathscrA_V connected to V. It is proved that V is isomorphic to V' over k (algebraic closure of k, resp.) if and only if \mathscrA_V is isomorphic (Morita equivalent, resp.) to \mathscrA_V'. In particular, the Morita equivalent C^*-algebras \mathscrA_V parametrize twists of the variety V. The case of rational elliptic curves is considered in detail.

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