Supersingular P-adic L-functions, Maass-shimura Operators and Waldspurger Formulas: Ams-212 - Brossura

Kriz, Daniel J.

Brossura

ISBN 10: 0691216460 ISBN 13: 9780691216461

Casa editrice: Princeton Univ Pr, 2021

Riassunto

A groundbreaking contribution to number theory that unifies classical and modern results

This book develops a new theory of p-adic modular forms on modular curves, extending Katz's classical theory to the supersingular locus. The main novelty is to move to infinite level and extend coefficients to period sheaves coming from relative p-adic Hodge theory. This makes it possible to trivialize the Hodge bundle on the infinite-level modular curve by a "canonical differential" that restricts to the Katz canonical differential on the ordinary Igusa tower. Daniel Kriz defines generalized p-adic modular forms as sections of relative period sheaves transforming under the Galois group of the modular curve by weight characters. He introduces the fundamental de Rham period, measuring the position of the Hodge filtration in relative de Rham cohomology. This period can be viewed as a counterpart to Scholze's Hodge-Tate period, and the two periods satisfy a Legendre-type relation. Using these periods, Kriz constructs splittings of the Hodge filtration on the infinite-level modular curve, defining p-adic Maass-Shimura operators that act on generalized p-adic modular forms as weight-raising operators. Through analysis of the p-adic properties of these Maass-Shimura operators, he constructs new p-adic L-functions interpolating central critical Rankin-Selberg L-values, giving analogues of the p-adic L-functions of Katz, Bertolini-Darmon-Prasanna, and Liu-Zhang-Zhang for imaginary quadratic fields in which p is inert or ramified. These p-adic L-functions yield new p-adic Waldspurger formulas at special values.

Su questo libro

Informazioni sull'autore

Daniel J. Kriz is an instructor in pure mathematics and a National Science Foundation postdoctoral fellow at the Massachusetts Institute of Technology.

Dettagli dell'edizione

• Editore: Princeton Univ Pr
• Data di pubblicazione: 2021
• Lingua: Inglese
• ISBN 10: 0691216460
• ISBN 13: 9780691216461
• Rilegatura: Copertina flessibile
• Numero di pagine: 258
• Contatto del produttore: Princeton University Press; https://press.princeton.edu/books; ; 7th Floor, New South Building; PRINCETON; NJ; 8544; U.S.A.
• Persona responsabile: GPSR Kontakt; gpsr@libri.de; ; Europaallee 1; Bad Hersfeld; 36244; Germania