Seminario Teoría de Números

Title: On the Artin formalism for Garrett-Rankin p-adic L-functions

SPEAKER: Daniele Casazza (University College Dublin)

DATE & TIME: Miércoles 01 de febrero - 16:30

VENUE: Aula 420, Departamento de Matemáticas, UAM.

ABSTRACT: In the last decade, the Garrett-Rankin p-adic L-function associated with a triple of modular forms (f,g,h) has been studied by many authors because of its connection with diagonal cycles, which makes it relevant in the study of the Birch and Swinnerton-Dyer conjecture. In our work we study how the Artin formalism translates in the p-adic setting when h=g*, and the central critical motive associated with the triple (f,g,g*) therefore splits as a direct sum. The shape of the factorization of p-adic L-functions that we obtain reminds of previous results in different contexts by Dasgupta, Palvannan, and Gross. However, their setting contains non-critical motives in stark contrast to ours, and our factorization is veryt irregular in the Perrin-Riou framework. This is the first occurrence of this type of phenomenon, and we interpret it in the context of what we call "the Bertolini-Darmon-Prasanna philosophy", where p-adic L-function play the role of p-adic avatars of the derivative of their complex counterpart. This work is joint with K. Büyükboduk and R. Sakamoto.