Hodge-Tate and de Rham representations in the imperfect residue field case

Morita, Kazuma. "Hodge-Tate and de Rham representations in the imperfect residue field case." Annales scientifiques de l'École Normale Supérieure 43.2 (2010): 341-355. <http://eudml.org/doc/272211>.

@article{Morita2010,
abstract = {Let $K$ be a $p$-adic local field with residue field $k$ such that $[k : k^p] = p^e &lt; +\infty $ and $V$ be a $p$-adic representation of $\text\{\rm Gal\}(\overline\{K\}/K)$. Then, by using the theory of $p$-adic differential modules, we show that $V$ is a Hodge-Tate (resp. de Rham) representation of $\text\{\rm Gal\}(\overline\{K\}/K)$ if and only if $V$ is a Hodge-Tate (resp. de Rham) representation of $\text\{\rm Gal\}(\overline\{K^\{\text\{\rm pf\}\}\}/K^\{\text\{\rm pf\}\})$ where $K^\{\text\{\rm pf\}\}/K$ is a certain $p$-adic local field with residue field the smallest perfect field $k^\{\text\{\rm pf\}\}$ containing $k$.},
author = {Morita, Kazuma},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {$p$-adic Galois representation; $p$-adic cohomology; $p$-adic differential equation},
language = {eng},
number = {2},
pages = {341-355},
publisher = {Société mathématique de France},
title = {Hodge-Tate and de Rham representations in the imperfect residue field case},
url = {http://eudml.org/doc/272211},
volume = {43},
year = {2010},
}

TY - JOUR
AU - Morita, Kazuma
TI - Hodge-Tate and de Rham representations in the imperfect residue field case
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2010
PB - Société mathématique de France
VL - 43
IS - 2
SP - 341
EP - 355
AB - Let $K$ be a $p$-adic local field with residue field $k$ such that $[k : k^p] = p^e &lt; +\infty $ and $V$ be a $p$-adic representation of $\text{\rm Gal}(\overline{K}/K)$. Then, by using the theory of $p$-adic differential modules, we show that $V$ is a Hodge-Tate (resp. de Rham) representation of $\text{\rm Gal}(\overline{K}/K)$ if and only if $V$ is a Hodge-Tate (resp. de Rham) representation of $\text{\rm Gal}(\overline{K^{\text{\rm pf}}}/K^{\text{\rm pf}})$ where $K^{\text{\rm pf}}/K$ is a certain $p$-adic local field with residue field the smallest perfect field $k^{\text{\rm pf}}$ containing $k$.
LA - eng
KW - $p$-adic Galois representation; $p$-adic cohomology; $p$-adic differential equation
UR - http://eudml.org/doc/272211
ER -