Homology, Homotopy and Applications

Volume 5 (2003)

Number 1

Weak corestriction principle for non-abelian Galois cohomology

Pages: 219 – 249

DOI: http://dx.doi.org/10.4310/HHA.2003.v5.n1.a10

Author

Nguyêñ Quôć Thǎńg (Institute of Mathematics, Hanoi, Vietnam)

Abstract

We introduce the notion of (Weak) Corestriction Principle and prove some relations between the validity of this principle for various connecting maps in non-abelian Galois cohomology over fields of characteristic 0. We also prove the validity of Weak Corestriction Principle for images of coboundary maps $H^1(k,G) \to H^2(k,T)$, where $T$ is a finite commutative $k$-group of multiplicative type, $G$ is adjoint, semisimple and contains only almost simple factors of certain inner types.

Keywords

corestriction maps, Norm maps, Non-abelian Galois cohomology

2010 Mathematics Subject Classification

Primary 11Gxx. Secondary 18G50, 20G10.

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