Almost étale extensions of Fontaine rings and log-crystalline cohomology in the semi-stable reduction case

Rémi Shankar Lodh[1]

  • [1] The University of Utah Department of Mathematics 155 S 1400 E Salt Lake City UT 84112 (USA)

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 5, page 1875-1942
  • ISSN: 0373-0956

Abstract

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Let K be a field of characteristic zero complete for a discrete valuation, with perfect residue field of characteristic p > 0 , and let K + be the valuation ring of K . We relate the log-crystalline cohomology of the special fibre of certain affine K + -schemes X = Spec ( R ) with good or semi-stable reduction to the Galois cohomology of the fundamental group π 1 ( X K ¯ ) of the geometric generic fibre with coefficients in a Fontaine ring constructed from R . This is based on Faltings’ theory of almost étale extensions.

How to cite

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Lodh, Rémi Shankar. "Almost étale extensions of Fontaine rings and log-crystalline cohomology in the semi-stable reduction case." Annales de l’institut Fourier 61.5 (2011): 1875-1942. <http://eudml.org/doc/219736>.

@article{Lodh2011,
abstract = {Let $K$ be a field of characteristic zero complete for a discrete valuation, with perfect residue field of characteristic $p&gt;0$, and let $K^+$ be the valuation ring of $K$. We relate the log-crystalline cohomology of the special fibre of certain affine $K^+$-schemes $X=\operatorname\{Spec\}(R)$ with good or semi-stable reduction to the Galois cohomology of the fundamental group $\pi _1(X_\{\bar\{K\}\})$ of the geometric generic fibre with coefficients in a Fontaine ring constructed from $R$. This is based on Faltings’ theory of almost étale extensions.},
affiliation = {The University of Utah Department of Mathematics 155 S 1400 E Salt Lake City UT 84112 (USA)},
author = {Lodh, Rémi Shankar},
journal = {Annales de l’institut Fourier},
keywords = {$p$-adic Hodge theory; almost étale extensions; crystalline cohomology; log-structures; -adic Hodge theory},
language = {eng},
number = {5},
pages = {1875-1942},
publisher = {Association des Annales de l’institut Fourier},
title = {Almost étale extensions of Fontaine rings and log-crystalline cohomology in the semi-stable reduction case},
url = {http://eudml.org/doc/219736},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Lodh, Rémi Shankar
TI - Almost étale extensions of Fontaine rings and log-crystalline cohomology in the semi-stable reduction case
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 5
SP - 1875
EP - 1942
AB - Let $K$ be a field of characteristic zero complete for a discrete valuation, with perfect residue field of characteristic $p&gt;0$, and let $K^+$ be the valuation ring of $K$. We relate the log-crystalline cohomology of the special fibre of certain affine $K^+$-schemes $X=\operatorname{Spec}(R)$ with good or semi-stable reduction to the Galois cohomology of the fundamental group $\pi _1(X_{\bar{K}})$ of the geometric generic fibre with coefficients in a Fontaine ring constructed from $R$. This is based on Faltings’ theory of almost étale extensions.
LA - eng
KW - $p$-adic Hodge theory; almost étale extensions; crystalline cohomology; log-structures; -adic Hodge theory
UR - http://eudml.org/doc/219736
ER -

References

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