On component groups of Jacobians of Drinfeld modular curves

Mihran Papikian

Displaying similar documents to “On component groups of Jacobians of Drinfeld modular curves”

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.

The Mumford-Tate group of 1-motives

Cristiana Bertolin (2002)

Annales de l’institut Fourier

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In this paper we study the structure and the degeneracies of the Mumford-Tate group $M T (M)$ of a 1-motive $M$ defined over $ℂ$ . This group is an algebraic $ℚ$ - group acting on the Hodge realization of $M$ and endowed with an increasing filtration $W_{•}$ . We prove that the unipotent radical of $M T (M)$ , which is $W_{- 1} (M T (M))$ , injects into a “generalized” Heisenberg group. We then explain how to reduce to the study of the Mumford-Tate group of a direct sum of 1-motives whose torus’character group and whose lattice are both...

Group Schemes over artinian rings and Applications

Ioan Berbec (2009)

Annales de l’institut Fourier

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Let $n$ be a positive integer and $A^{'}$ a complete characteristic zero discrete valuation ring with maximal ideal $𝔪$ , absolute ramification index $e < p - 1$ and perfect residue field $k$ of characteristic $p > 2$ . In this paper we classify smooth finite dimensional formal $p$ - groups over $A_{n}^{'} = A^{'} / 𝔪^{n} A^{'}$ , groups on which the “multiplication by $p$ ” morphism is faithfully flat, in particular $p$ -divisible groups. As applications, we prove that $p$ -divisible groups over $k$ , and the morphisms between them, lift canonically to $A^{'} / p A^{'}$ , and...

Minimal resolution and stable reduction of $X_{0} (N)$

Bas Edixhoven (1990)

Annales de l'institut Fourier

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Let $N \geq 1$ be an integer. Let $X_{0} (N)$ be the modular curve over $Z$ , as constructed by Katz and Mazur. The minimal resolution of $X_{0} (N)$ over $Z [1 / 6]$ is computed. Let $p \geq 5$ be a prime, such that $N = p^{2} M$ , with $M$ prime to $p$ . Let $n = (p^{2} - 1) / 2$ . It is shown that $X_{0} (N)$ has stable reduction at $p$ over $Q [\sqrt[n]{p}]$ , and the fibre at $p$ of the stable model is computed.

The Brauer group of torsors and its arithmetic applications

David Harari, Alexei N. Skorobogatov (2003)

Annales de l'Institut Fourier

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Let $X$ be an algebraic variety defined over a field $k$ of characteristic $0$ , and let $Y$ be an $X$ -torsor under a torus. We compute the Brauer group of $Y$ . In the case of a number field $k$ we deduce results concerning the arithmetic of $X$ .

Displaying similar documents to “On component groups of Jacobians of Drinfeld modular curves”

Tamely ramified Hida theory

The Mumford-Tate group of 1-motives

Group Schemes over artinian rings and Applications

Minimal resolution and stable reduction of X 0 ( N )

The Brauer group of torsors and its arithmetic applications

Minimal resolution and stable reduction of $X_{0} (N)$