Abstract. In this paper we establish the endoscopic classification of tempered representations of quasi-split unitary groups over local fields, and the endoscopic classification of the discrete automorphic spectrum of quasi-split unitary groups over global number fields. The method is analogous to the work of Arthur [A1] on orthogonal and symplectic groups, based on the theory of endoscopy and the comparison of trace formulas on unitary groups and general linear groups.

In this paper we generalize the work of Harris-Soudry-Taylor and construct the compatible systems of two-dimensional Galois representations attached to cuspidal automorphic representations of cohomological type on GL 2 over a CM field with a suitable condition on their central characters. We also prove a local-global compatibility statement, up to semi-simplification.

Using a p-adic analogue of the convolution method of Rankin-Selberg and Shimura, we construct the two-variable p-adic L-function of a Hida family of Hilbert modular eigenforms of parallel weight. It is shown that the conditions of Greenberg-Stevens [R. Greenberg and G. Stevens, p-adic L-functions and p-adic periods of modular forms, Invent. Math. 111 (1993), are satisfied, from which we deduce special cases of the Mazur-Tate-Teitelbaum conjecture in the Hilbert modular setting.

Abstract. For an elliptic curve E over Q satisfying suitable hypotheses, Bertolini and Darmon have derived a formula for the Heegner point on E in terms of the central derivative of the two variable p-adic L-function associated to E. In this paper, we generalize their work to the setting of totally real fields in which p is inert. We also use this generalization to improve the results obtained by Bertolini-Darmon in the case of an elliptic curve defined over the field of rational numbers. Mathematics Subject Classification (2010). 11G40, 11F33.

No abstract