Reduction modulo $p$ of certain semi-stable representations
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.
متن کاملEXPLICIT REDUCTION MODULO p OF CERTAIN 2-DIMENSIONAL CRYSTALLINE REPRESENTATIONS, II
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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Let p be an odd prime, K a finite extension of Qp, GK = Gal(K̄/K) its absolute Galois group and e = e(K/Qp) its absolute ramification index. Suppose that T is a p-torsion representation of GK that is isomorphic to a quotient of GK -stable Zp-lattices in a semi-stable representation with HodgeTate weights {0, . . . , r}. We prove that there exists a constant μ depending only on n, e and r such th...
متن کاملQuasi-semi-stable representations
Fix K a p-adic field and denote by GK its absolute Galois group. Let K∞ be the extension of K obtained by adding p-th roots of a fixed uniformizer, and G∞ ⊂ GK its absolute Galois group. In this article, we define a class of p-adic torsion representations of G∞, named quasi-semi-stable. We prove that these representations are “explicitly” described by a certain category of linear algebra object...
متن کاملREDUCTION MODULO p OF CUSPIDAL REPRESENTATIONS AND WEIGHTS IN SERRE’S CONJECTURE
Let O be the ring of integers of a p-adic field and p its maximal ideal. We compute the Jordan-Hölder decomposition of the reduction modulo p of the cuspidal representations of GL2(O/p) for e ≥ 1. We also provide an alternative formulation of Serre’s conjecture for Hilbert modular forms. 1. Cuspidal representations and weights 1.1. Cuspidal representations. Let K/Qp be a local field, where p is...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2017
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/6827