Displaying similar documents to “On Galois H -objects and invertible H * -modules”

Galois H-objects with a normal basis in closed categories. A cohomological interpretation.

José N. Alonso Alvarez, José Manuel Fernández Vilaboa (1993)

Publicacions Matemàtiques

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In this paper, for a cocommutative Hopf algebra H in a symmetric closed category C with basic object K, we get an isomorphism between the group of isomorphism classes of Galois H-objects with a normal basis and the second cohomology group H2(H,K) of H with coefficients in K. Using this result, we obtain a direct sum decomposition for the Brauer group of H-module Azumaya monoids with inner action: BMinn(C,H) ≅ B(C) ⊕ H2...

Homotopy theory of Hopf Galois extensions

Christian Kassel, Hans-Jürgen Schneider (2005)

Annales de l'institut Fourier

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We introduce the concept of homotopy equivalence for Hopf Galois extensions and make a systematic study of it. As an application we determine all H -Galois extensions up to homotopy equivalence in the case when H is a Drinfeld-Jimbo quantum group.

Galois theory of q -difference equations

Marius van der Put, Marc Reversat (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

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Choose q ∈ ℂ with 0 < | q | < 1 . The main theme of this paper is the study of linear q -difference equations over the field K of germs of meromorphic functions at 0 . A systematic treatment of classification and moduli is developed. It turns out that a difference module M over K induces in a functorial way a vector bundle v ( M ) on the Tate curve E q : = ℂ * / q ℤ that was known for modules with ”integer slopes“, [Saul, 2]). As a corollary one rediscovers Atiyah’s classification ( [ A t ] ) of the indecomposable vector bundles on the...

Galois structure of ideals in wildly ramified abelian p -extensions of a p -adic field, and some applications

Nigel P. Byott (1997)

Journal de théorie des nombres de Bordeaux

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Let K be a finite extension of ℚ p with ramification index e , and let L / K be a finite abelian p -extension with Galois group Γ and ramification index p n . We give a criterion in terms of the ramification numbers t i for a fractional ideal 𝔓 h of the valuation ring S of L not to be free over its associated order 𝔄 ( K Γ ; 𝔓 h ) . In particular, if t n - [ t n / p ] < p n - 1 e then the inverse different can be free over its associated order only when t i ≡ - 1 (mod p n ) for all i . We give three consequences of this. Firstly, if 𝔄 ( K Γ ; S ) is a Hopf order and...