David Loeffler

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The main result of this paper is an instance of the conjecture made by Gouvêa and Mazur in [GM95], which asserts that for certain values of r the space of r-overconvergent p-adic modular forms of tame level N and weight k should be spanned by the finite slope Hecke eigenforms. For N = 1, p = 2 and k = 0 we show that this follows from the combinatorial(More)
I present a general theory of overconvergent p-adic automorphic forms and eigenvarieties for connected reductive algebraic groups G whose real points are compact modulo centre, extending earlier constructions for forms of GLn due to Buzzard, Chenevier and Yamagami. This leads to some new phenomena, including the appearance of intermediate spaces of(More)
Let p be a prime number. It’s well known that classical modular Hecke eigenforms can satisfy nontrivial congruence relations modulo powers of p; for example the standard Eisenstein seriesEk satisfiesEp−1 = 1 (mod p), and more generally E(p−1)pr = 1 (mod p) for all integers r ≥ 0. We’d like to construct some kind of p-adic space of modular forms in which(More)
This paper studies Emerton’s Jacquet module functor for locally analytic representations of p-adic reductive groups, introduced in [Eme06a]. When P is a parabolic subgroup whose Levi factor M is not commutative, we show that passing to an isotypical subspace for the derived subgroup ofM gives rise to essentially admissible locally analytic representations(More)
The theory of spectra for Banach algebras is outlined, including the Gelfand-Nǎımark theorem for commutative B∗-algebras. Resolutions of the identity are introduced, with examples; finally, we prove the spectral theorem for bounded normal operators on a Hilbert space, and conclude with some applications.
This paper studies Emerton’s Jacquet module functor<lb>for locally analytic representations of p-adic reductive groups, intro-<lb>duced in [Eme06a]. When P is a parabolic subgroup whose Levi<lb>factor M is not commutative, we show that passing to an isotypical<lb>subspace for the derived subgroup ofM gives rise to essentially admis-<lb>sible locally(More)
Proposition 4.1 (1) of this article is not correct as stated. For instance, if ε is the quadratic Dirichlet character of conductor 15, then there are two newforms in Sk(Γ1(15), ε) with coefficients in Q, and these are twists of each other by the quadratic character of conductor 3, whereas the quantity u in the proposition is 0 here. I am grateful to Steve(More)