Explicit reduction modulo p of certain 2-dimensional crystalline representations, II
نویسندگان
چکیده
منابع مشابه
Explicit reduction modulo p of certain 2-dimensional crystalline representations
We use the p-adic local Langlands correspondence for GL2(Qp) to explicitly compute the reduction modulo p of certain 2-dimensional crystalline representations of small slope, and give applications to modular forms.
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We complete the calculations begun in [BG09], using the p-adic local Langlands correspondence for GL2(Qp) to give a complete description of the reduction modulo p of the 2-dimensional crystalline representations of GQp of slope less than 1, when p > 2.
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— We give an algorithm for computing the reduction modulo p of 2-dimensional crystalline representations of Gal(Q p /Qp). This algorithm relies on Fontaine’s theory of (φ,Γ)-modules as well as the theory of Wach modules. It is rather explicit and can be implemented using standard mathematical software.
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To each real semisimple Jordan algebra, the Tits-Koecher-Kantor theory associates a distinguished parabolic subgroup P = L N of a semisimple Lie group G. The groups P which arise in this manner are precisely those for which N is abelian, and P is conjugate to its opposite P. Each non-open L-orbit O on N∗ admits an L-equivariant measure dμ which is unique up to scalar multiple. By Mackey theory,...
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— We construct explicitly some analytic families of étale (φ,Γ)-modules, which give rise to analytic families of 2-dimensional crystalline representations. As an application of our constructions, we verify some conjectures of Breuil on the reduction modulo p of those representations, and extend some results (of Deligne, Edixhoven, Fontaine and Serre) on the representations arising from modular ...
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ژورنال
عنوان ژورنال: Bulletin of the London Mathematical Society
سال: 2013
ISSN: 0024-6093
DOI: 10.1112/blms/bds128