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Congruence modules in higher codimension and zeta lines in Galois cohomology

Autor: Iyengar, Srikanth B., Khare, Chandrashekhar B., Manning, Jeffrey, Urban, Eric

This work builds on earlier work of the first three authors where a notion of congruence modules in higher codimension is introduced. The main new results are a criterion for detecting regularity of local rings in terms of congruence modules, and a m

Externí odkaz: http://arxiv.org/abs/2311.13070

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On Euler systems for adjoint Hilbert modular Galois representations

Autor: Urban, Eric

We prove the existence of Euler systems for adjoint modular Galois representations using deformations of Galois representations coming from Hilbert modular forms and relate them to $p$-adic $L$-functions under a conjectural formula for the Fitting id

Externí odkaz: http://arxiv.org/abs/2102.06305

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Integral period relations and congruences

Autor: Tilouine, Jacques, Urban, Eric

Under relatively mild and natural conditions, we establish an integral period relations for the (real or imaginary) quadratic base change of an elliptic cusp form. This answers a conjecture of Hida regarding the {\it congruence number} controlling th

Externí odkaz: http://arxiv.org/abs/1811.11166

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Akademický článek

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Several variable p-adic families of Siegel-Hilbert cusp eigensystems and their Galois representations

Autor: Tilouine, Jacques, Urban, Eric

Let F be a totally real field and G=GSp(4)_{/F}. In this paper, we show under a weak assumption that, given a Hecke eigensystem lambda which is (p,P)-ordinary for a fixed parabolic P in G, there exists a several variable p-adic family underline{lambd

Externí odkaz: http://arxiv.org/abs/math/9901156

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Selmer groups and the Eisenstein-Klingen ideal

Autor: Urban, Eric

In this article, we set up a strategy to prove one divisibility towards the main Iwasawa conjecture for the Selmer groups attached to the twisted adjoint modular Galois representations associated to Hida families. This conjecture asserts the equality

Externí odkaz: http://arxiv.org/abs/math/9803171

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