• Corpus ID: 119325058

# On Perrin-Riou's exponential map for $(\varphi, \Gamma)$-modules

@article{Riedel2016OnPE,
title={On Perrin-Riou's exponential map for \$(\varphi, \Gamma)\$-modules},
author={Andreas Riedel},
journal={arXiv: Number Theory},
year={2016}
}
• Andreas Riedel
• Published 20 September 2016
• Mathematics
• arXiv: Number Theory
Let $K / \mathbb{Q}_p$ be a finite Galois extension and $D$ a $(\varphi, \Gamma)$-module over the Robba-ring $B^{\dagger}_{\textrm{rig}, K}$. We give a generalization of the Bloch-Kato exponential map for $D$ using continuous Galois-cohomology groups $H^i(G_K, W(D))$ for the $B$-pair $W(D)$ associated to $D$. We construct a big exponential map $\Omega_{D,h}$ ($h \in \mathbb{N}$) for cyclotomic extensions of $K$ for $D$ in the style of Perrin-Riou using the theory of Berger's $B$-pairs, which…

## References

SHOWING 1-10 OF 32 REFERENCES

• L. Berger
• Mathematics
Compositio Mathematica
• 2009
Abstract Colmez has given a recipe to associate a smooth modular representation Ω(W) of the Borel subgroup of GL2(Qp) to a $\overline {\mathbf {F}}_p$-representation W of \$\mathrm {Gal}(\overline
In the first part, we introduce theory of p-adic analysis for one variable p-adic functions and then use them to construct Kubota-Leopoldt p-adic L-functions. In the second part, we give a
Abstract.In this paper, we associate to every p-adic representation V a p-adic differential equation D†rig(V), that is to say a module with a connection over the Robba ring. We do this via the theory
• Mathematics
• 2007
A. Lascoux: Anneau de Grothendieck de la variete de drapeaux S. Lichtenbaum: New Results on Weight-Two Motivic Cohomology G. Lusztig: Symmetric Spaces over a Finite Field Z. Mebkhout: Le theoreme de
• Mathematics
• 2006
In this paper, given a smooth proper scheme X over a p-adic dvr and a p-power torsionlocal system L on it, we study a family of sheaves associated to the cohomology of local, relative (',)-modules of
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
We study the category of B-pairs (W_e,W_dR^+) where W_e is a free B_cris^{phi=1}-module with a semilinear and continuous action of G_K and where W_dR^+ is a G_K-stable B_dR^+ -lattice in B_dR \otimes