Curves and their fundamental groups

Gerd Faltings

Displaying similar documents to “Curves and their fundamental groups”

$W C$ -groups over $p$ -adic fields

J. Tate (1956-1958)

Séminaire Bourbaki

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On the Euler-Poincaré characteristics of finite dimensional $p$ -adic Galois representations

John Coates, Ramdorai Sujatha, Jean-Pierre Wintenberger (2001)

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Problems from the workshop on Automorphisms of Curves (Leiden, August, 2004)

Gunther Cornelissen, Frans Oort (2005)

Rendiconti del Seminario Matematico della Università di Padova

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In the week of August, 16th-20th of 2004, we organized a workshop about “Automorphisms of Curves” at the Lorentz Center in Leiden. The programme included two “problem sessions”. Some of the problems presented at the workshop were written down; this is our edition of these refereed and revised papers. Edited by Gunther Cornelissen and Frans Oort with contributions of I. Bouw; T. Chinburg; G. Cornelissen; C. Gasbarri; D. Glass; C. Lehr; M. Matignon; F. Oort; R. Pries; S. Wewers. ...

Rational connectedness and Galois covers of the projective line.

Colliot-Thélène, Jean-Louis (2000)

Annals of Mathematics. Second Series

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On the conjectures of Birch and Swinnerton-Dyer and a geometric analog

John Tate (1964-1966)

Séminaire Bourbaki

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On certain Galois representations related to the modular curve $X_{1} (p)$

Ehud De Shalit (1995)

Compositio Mathematica

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Tamely ramified Hida theory

Assaf Goldberger, Ehud de Shalit (2002)

Annales de l’institut Fourier

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Let $J_{1}$ be the Jacobian of the modular curve associated with $Γ_{1} (N p), (p, N) = 1$ and $J_{0}$ the one associated with $Γ_{1} (N) \cap Γ_{0} (p)$ . We study $J_{1} [p - 1]$ as a Hecke and Galois-module. We relate a certain matrix of $p$ -adic periods to the infinitesimal deformation of the $U_{p}$ -operator.

Local-to-global extensions of representations of fundamental groups

Nicholas M. Katz (1986)

Annales de l'institut Fourier

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Let $K$ be a field of characteristic $p > 0$ , $C$ a proper, smooth, geometrically connected curve over $K$ , and 0 and $\infty$ two $K$ -rational points on $C$ . We show that any representation of the local Galois group at $\infty$ extends to a representation of the fundamental group of $C - {0, \infty}$ which is tamely ramified at 0, provided either that $K$ is separately closed or that $C$ is $P^{1}$ . In the latter case, we show there exists a unique such extension, called “canonical”, with the property that the image of the geometric fundamental...