Cohomology and self-dual normal bases for infinite Galois field extensions

Cohomological Invariants for G - Galois Algebras and Self - Dual Normal Bases

We define degree two cohomological invariants for GGalois algebras over fields of characteristic not 2, and use them to give necessary conditions for the existence of a self–dual normal basis. In some cases (for instance, when the field has cohomological dimension ≤ 2) we show that these conditions are also sufficient.

Hochschild-Mitchell cohomology and Galois extensions

We define H-Galois extensions for k-linear categories and prove the existence of a Grothendieck spectral sequence for Hochschild-Mitchell cohomology related to this situation. This spectral sequence is multiplicative and for a group algebra decomposes as a direct sum indexed by conjugacy classes of the group. We also compute some Hochschild-Mitchell cohomology groups of categories with infinite...

Construction of Self-Dual Integral Normal Bases in Abelian Extensions of Finite and Local Fields

Let F/E be a finite Galois extension of fields with abelian Galois group Γ. A self-dual normal basis for F/E is a normal basis with the additional property that TrF/E(g(x), h(x)) = δg,h for g, h ∈ Γ. Bayer-Fluckiger and Lenstra have shown that when char(E) 6= 2, then F admits a self-dual normal basis if and only if [F : E] is odd. If F/E is an extension of finite fields and char(E) = 2, then F ...

Finitary Galois Extensions over Noncommutative Bases

We study Galois extensions M (co-)H ⊂ M for H-(co)module algebras M if H is a Frobenius Hopf algebroid. The relation between the action and coaction pictures is analogous to that found in Hopf-Galois theory for finite dimensional Hopf algebras over fields. So we obtain generalizations of various classical theorems of Kreimer-Takeuchi, Doi-Takeuchi and Cohen-FischmanMontgomery. We find that the ...

Galois Theory for Arbitrary Field Extensions