New methods for $$(\varphi, \Gamma)$$ ( φ , Γ ) -modules
نویسندگان
چکیده
منابع مشابه
New 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 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 Families of (φ,Γ)-modules
We prove that every family of (overconvergent) étale (φ,Γ)-modules over a reduced affinoid algebra can be locally converted to a family of p-adic representations uniquely.
متن کاملSlope filtrations and (φ,Γ)-modules in families
These are the notes for a three-lecture minicourse given at the Institut Henri Poincaré in January 2010 as part of the Galois Trimester. The first lecture reviews the theory of slopes and slope filtrations for Frobenius actions (φ-modules) over the Robba ring, the link to p-adic Hodge theory via the work of Berger, and the analogue of Dieudonné-Manin classifications over the Robba ring. The sec...
متن کاملExtensions of Rank One (φ,γ)-modules and Crystalline Representations
Let K be a finite unramified extension of Qp. We parametrize the (φ, Γ)-modules corresponding to reducible two-dimensional Fp-representations of GK and characterize those which have reducible crystalline lifts with certain Hodge-Tate weights.
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: Research in the Mathematical Sciences
سال: 2015
ISSN: 2197-9847
DOI: 10.1186/s40687-015-0031-z