Cohomology and Duality for (φ, Γ)-modules over the Robba Ring
نویسندگان
چکیده
منابع مشابه
Cohomology and duality for (φ,Γ)-modules over the Robba ring
Given a p-adic representation of the Galois group of a local field, we show that its Galois cohomology can be computed using the associated étale (φ,Γ)-module over the Robba ring; this is a variant of a result of Herr. We then establish analogues, for not necessarily étale (φ,Γ)-modules over the Robba ring, of the Euler-Poincaré characteristic formula and Tate local duality for p-adic represent...
متن کامل6. Φ-Γ-modules and Galois cohomology
A method to solve it for G = GK (K is a local field) is to use Fontaine’s theory of ΦΓ-modules and pass to a simpler Galois representation, paying the price of enlarging Zp to the ring of integers of a two-dimensional local field. In doing this we have to replace linear with semi-linear actions. In this paper we give an overview of the applications of such techniques in different situations. We...
متن کاملOn the Slope Filtration of d - modules over the Robba Ring
Given a p-adic representation of the Galois group of a local field, we show that its Galois cohomology can be computed using the associated 6tale (o, F)-module over the Robba ring; this is a variant of a result of Herr. We then establish analogues, for not necessarily etale (ý, F)-modules over the Robba ring, of the Euler-Poincard characteristic formula and Tate local duality for p-adic represe...
متن کاملThe Cohomology of Modules over a Complete Intersection Ring
We investigate the cohomology of modules over commutative complete intersection rings. The first main result is that if M is an arbitrary module over a complete intersection ring R, and if Ext 2n R (M, M) = 0 for some n ≥ 1 then M has finite projective dimension. The second main result gives a new proof of the fact that the support variety of a Cohen-Macaulay module whose completion is indecomp...
متن کاملNew Methods for (φ,γ)-modules
Let p be a prime number. The subject of p-adic Hodge theory concerns the interplay between different objects arising from the cohomology of algebraic varieties over p-adic fields. A good introduction to the subject can be found in the notes of Brinon and Conrad [3]; here, we limit discussion to two proofs which we feel are simpler than their counterparts in the literature. Our original motivati...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: International Mathematics Research Notices
سال: 2007
ISSN: 1687-0247,1073-7928
DOI: 10.1093/imrn/rnm150