On Galois action in rigid DAHA modules

GALOIS p-GROUPS AND GALOIS MODULES

The smallest non-abelian p-groups play a fundamental role in the theory of Galois p-extensions. We illustrate this by highlighting their role in the definition of the norm residue map in Galois cohomology. We then determine how often these groups — as well as other closely related, larger p-groups — occur as Galois groups over given base fields. We show further how the appearance of some Galois...

On Modules Associated to Coalgebra Galois Extensions

For a given entwining structure (A,C)ψ involving an algebra A, a coalgebra C, and an entwining map ψ : C ⊗ A → A ⊗ C, a category MA(ψ) of right (A,C)ψmodules is defined and its structure analysed. In particular, the notion of a measuring of (A,C)ψ to (Ã, C̃)ψ̃ is introduced, and certain functors between M C A(ψ) and M Ã (ψ̃) induced by such a measuring are defined. It is shown that these functors ...

Galois Modules Arising from Faltings’s Strict Modules

Suppose O is a complete discrete valuation ring of positive characteristic with perfect residue field. The category of finite flat strict modules was recently introduced by Faltings and appears as an equal characteristic analogue of the classical category of finite flat group schemes. In this paper we obtain a classification of these modules and apply it to prove analogues of properties, which ...

Galois Action on Class Groups

It is well known that the Galois group of an extension L/F puts constraints on the structure of the relative ideal class group Cl(L/F ). Explicit results, however, hardly ever go beyond the semisimple abelian case, where L/F is abelian (in general cyclic) and where (L : F ) and #Cl(L/F ) are coprime. Using only basic parts of the theory of group representations, we give a unified approach to th...

Rigid Mixin Modules