Relative p-adic Hodge theory, II: Imperfect period rings

KS Kedlaya, R Liu - arXiv preprint arXiv:1602.06899, 2016 - arxiv.org
In a previous paper, we constructed a category of (phi, Gamma)-modules associated to any
adic space over Q_p with the property that the etale (phi, Gamma)-modules correspond to …

Syntomic complexes and p-adic nearby cycles

P Colmez, W Nizioł - Inventiones mathematicae, 2017 - Springer
We compute syntomic cohomology of semistable affinoids in terms of cohomology of (φ,
Γ)(φ, Γ)-modules which, thanks to work of Fontaine–Herr, Andreatta–Iovita, and Kedlaya …

Analytic families of finite-slope Selmer groups

J Pottharst - Algebra & Number Theory, 2013 - msp.org
We develop a theory of Selmer groups for analytic families of Galois representations, which
are only assumed “ordinary” on the level of their underlying (φ, Γ)-modules. Our approach …

Overconvergent Eichler–Shimura isomorphisms

F Andreatta, A Iovita, G Stevens - … of the Institute of Mathematics of …, 2015 - cambridge.org
OVERCONVERGENT EICHLER–SHIMURA ISOMORPHISMS Page 1 221 doi:10.1017/S1474748013000364
c Cambridge University Press 2013 OVERCONVERGENT EICHLER–SHIMURA …

Period spaces for Hodge structures in equal characteristic

U Hartl - Annals of mathematics, 2011 - JSTOR
We develop the analog in equal positive characteristic of Fontaine's theory for crystalline
Galois representations of a p-adic field. In particular we describe the analog of Fontaine's …

[PDF][PDF] Semistable sheaves and comparison isomorphisms in the semistable case

F Andreatta, A Iovita - … del Seminario Matematico della Università di …, 2012 - numdam.org
Semistable Sheaves and Comparison Isomorphisms in the Semistable Case Page 1 Rend.
Sem. Mat. Univ. Padova, Vol. 128 (2012) Semistable Sheaves and Comparison Isomorphisms …

Comparison isomorphisms for smooth formal schemes

F Andreatta, A Iovita - Journal of the Institute of Mathematics of …, 2013 - cambridge.org
Let p> 0 denote a prime integer and K a complete discrete valuation field of characteristic 0
and perfect residue field k of characteristic p. This article proposes a new point of view on …

Analytic Geometry and Hodge-Frobenius Structure

X Tong - arXiv preprint arXiv:2011.08358, 2020 - arxiv.org
In this paper, we study Frobenius structures in higher dimensional $ p $-adic analytic
geometry and the corresponding $ p $-adic functional analysis. This will build up …

[PDF][PDF] CMI Summer School notes on p-adic Hodge theory (preliminary version)

O Brinon, B Conrad - course notes, 2009 - math.bu.edu
3. Étale ϕ-modules 26 3.1. p-torsion representations 27 3.2. Torsion and lattice
representations 32 3.3. Qp-representations of GE 41 3.4. Exercises 43 4. Better ring …

-représentations dans le cas relatif

F Andreatta, O Brinon - Annales scientifiques de l'Ecole normale …, 2010 - numdam.org
Dans ce travail nous développons un analogue relatif de la théorie de Sen pour les B dR-
représentations. On donne des applications à la théorie des représentations p-adiques, en …