共查询到10条相似文献,搜索用时 46 毫秒
1.
Owen T.R. Jones 《Journal of Number Theory》2011,131(9):1616-1640
Let G be a connected reductive quasi-split algebraic group over a field L which is a finite extension of the p-adic numbers. We construct an exact sequence modelled on (the dual of) the BGG resolution involving locally analytic principal series representations for G(L). This leads to an exact sequence involving spaces of overconvergent p-adic automorphic forms for certain groups compact modulo centre at infinity. 相似文献
2.
We prove, over a p-adic local field F, that an irreducible supercuspidal representation of GL2n
(F) is a local Langlands functorial transfer from SO2n+1(F) if and only if it has a nonzero Shalika model (Corollary 5.2, Proposition 5.4 and Theorem 5.5). Based on this, we verify
(Sect. 6) in our cases a conjecture of Jacquet and Martin, a conjecture of Kim, and a conjecture of Speh in the theory of
automorphic forms. 相似文献
3.
Byeong-Kweon Oh 《manuscripta mathematica》2007,124(2):261-267
Let L, N and M be positive definite integral \({\mathbb{Z}}\) -lattices. In this paper, we show some relation between the weighted sum of representations of L and N by gen(M) and the weighted sum of extensions of \(\tilde M_{\tilde \sigma}\) in the gen(M σ) via N η when M is even and gcd(dL, dM) = 1. As a consequence of the particular case when M is even unimodular, we recapture the Böcherer formula (13) in (Böcherer, Maths Z 183:21–46, 1983) for the relation of the Fourier coefficients between Eisenstein series and Jacobi–Eisenstein series. 相似文献
4.
Sung Myung 《Advances in Mathematics》2006,199(2):331-355
The Bloch-Wigner function D2 is a single-valued version of a dilogarithm function and is used by Bloch to describe the Borel regulator map from K3(C) into R explicitly (c.f. [Bloch, Higher Regulators, Algebraic K-Theory, and Zeta Functions of Elliptic Curves, American Mathematical Society, Providence, RI, 2000]). We introduce a new way to formulate a single-valued dilogarithm function and use it to explicitly define a motivic regulator map for , defined in terms of the motivic complex of Goodwillie and Lichtenbaum. We also detect certain explicit nonzero elements in the motivic cohomology group. Throughout this paper, a path will be a C1-function from the unit interval [0,1] into C-{0}. 相似文献
5.
6.
Guy Henniart 《Inventiones Mathematicae》2000,139(2):439-455
Let F be a finite extension of ℚ
p
. For each integer n≥1, we construct a bijection from the set ?F
0
(n) of isomorphism classes of irreducible degree n representations of the (absolute) Weil group of F, onto the set ?
F
0
(n) of isomorphism classes of smooth irreducible supercuspidal representations of GL
n
(F). Those bijections preserve epsilon factors for pairs and hence we obtain a proof of the Langlands conjectures for GL
n
over F, which is more direct than Harris and Taylor’s. Our approach is global, and analogous to the derivation of local class field
theory from global class field theory. We start with a result of Kottwitz and Clozel on the good reduction of some Shimura
varieties and we use a trick of Harris, who constructs non-Galois automorphic induction in certain cases.
Oblatum 1-III-1999 & 21-VII-1999 / Published online: 29 November 1999 相似文献
7.
We study the restriction to smaller subgroups, of cohomology classes on arithmetic groups (possibly after moving the class
by Hecke correspondences), especially in the context of first cohomology of arithmetic groups. We obtain vanishing results for the first cohomology of cocompact arithmetic lattices in SU(n,1) which arise from hermitian forms over division algebras D of degree p
2, p an odd prime, equipped with an involution of the second kind. We show that it is not possible for a ‘naive’ restriction of
cohomology to be injective in general. We also establish that the restriction map is injective at the level of first cohomology
for non co-compact lattices, extending a result of Raghunathan and Venkataramana for co-compact lattices.
Received: 14 September 2000 / Accepted: 6 June 2001 相似文献
8.
Axel Ferrari 《manuscripta mathematica》2007,124(3):363-390
Our purpose is to obtain a geometric formula as explicit as possible for the L
2 index of a Dirac operator over a locally symmetric space of finite volume, generalizing Arthur’s formula for the Euler–Poincaré
caracteristic (Arthur in Invent Math 97:257–290, 1989). 相似文献
9.
We prove a Siegel type statement for finitely generated -submodules of under the action of a Drinfeld module . This provides a positive answer to a question we asked in a previous paper. We also prove an analog for Drinfeld modules
of a theorem of Silverman for nonconstant rational maps of over a number field. 相似文献
10.
Anton Deitmar 《Topology and its Applications》2006,153(14):2363-2381
A Lefschetz formula is given that relates loops in a regular finite graph to traces of a certain representation. As an application the vanishing orders of the Ihara/Bass zeta function are expressed as dimensions of global section spaces of locally constant sheaves. 相似文献