Covers in p -adic analytic geometry and log covers I: Cospecialization of the ( p ′ ) -tempered fundamental group for a family of curves

Emmanuel Lepage[1]

  • [1] Université Pierre et Marie Curie Institut Mathématique de Jussieu 4 place Jussieu 75005 PARIS (France)

Annales de l’institut Fourier (2013)

  • Volume: 63, Issue: 4, page 1427-1467
  • ISSN: 0373-0956

Abstract

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The tempered fundamental group of a p -adic analytic space classifies covers that are dominated by a topological cover (for the Berkovich topology) of a finite étale cover of the space. Here we construct cospecialization homomorphisms between ( p ′ ) versions of the tempered fundamental groups of the fibers of a smooth family of curves with semistable reduction. To do so, we will translate our problem in terms of cospecialization morphisms of fundamental groups of the log fibers of the log reduction and we will prove the invariance of the geometric log fundamental group of log smooth log schemes over a log point by change of log point.

How to cite

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Lepage, Emmanuel. "Covers in $p$-adic analytic geometry and log covers I: Cospecialization of the $(p^{\prime})$-tempered fundamental group for a family of curves." Annales de l’institut Fourier 63.4 (2013): 1427-1467. <http://eudml.org/doc/275554>.

@article{Lepage2013,
abstract = {The tempered fundamental group of a $p$-adic analytic space classifies covers that are dominated by a topological cover (for the Berkovich topology) of a finite étale cover of the space. Here we construct cospecialization homomorphisms between $(p^\{\prime\})$ versions of the tempered fundamental groups of the fibers of a smooth family of curves with semistable reduction. To do so, we will translate our problem in terms of cospecialization morphisms of fundamental groups of the log fibers of the log reduction and we will prove the invariance of the geometric log fundamental group of log smooth log schemes over a log point by change of log point.},
affiliation = {Université Pierre et Marie Curie Institut Mathématique de Jussieu 4 place Jussieu 75005 PARIS (France)},
author = {Lepage, Emmanuel},
journal = {Annales de l’institut Fourier},
keywords = {fundamental groups; Berkovich spaces; specialization},
language = {eng},
number = {4},
pages = {1427-1467},
publisher = {Association des Annales de l’institut Fourier},
title = {Covers in $p$-adic analytic geometry and log covers I: Cospecialization of the $(p^\{\prime\})$-tempered fundamental group for a family of curves},
url = {http://eudml.org/doc/275554},
volume = {63},
year = {2013},
}

TY - JOUR
AU - Lepage, Emmanuel
TI - Covers in $p$-adic analytic geometry and log covers I: Cospecialization of the $(p^{\prime})$-tempered fundamental group for a family of curves
JO - Annales de l’institut Fourier
PY - 2013
PB - Association des Annales de l’institut Fourier
VL - 63
IS - 4
SP - 1427
EP - 1467
AB - The tempered fundamental group of a $p$-adic analytic space classifies covers that are dominated by a topological cover (for the Berkovich topology) of a finite étale cover of the space. Here we construct cospecialization homomorphisms between $(p^{\prime})$ versions of the tempered fundamental groups of the fibers of a smooth family of curves with semistable reduction. To do so, we will translate our problem in terms of cospecialization morphisms of fundamental groups of the log fibers of the log reduction and we will prove the invariance of the geometric log fundamental group of log smooth log schemes over a log point by change of log point.
LA - eng
KW - fundamental groups; Berkovich spaces; specialization
UR - http://eudml.org/doc/275554
ER -

References

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