## Weak corestriction principle for non-Abelian Galois cohomology.(English)Zbl 1065.11021

Summary: 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 $$\text{H}^1(k,G) \to \text{H}^2(k,T)$$, 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.

### MSC:

 11E72 Galois cohomology of linear algebraic groups 18G50 Nonabelian homological algebra (category-theoretic aspects) 20G10 Cohomology theory for linear algebraic groups
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