Supersingular p-adic L-functions, Maass-Shimura Operators and Waldspurger Formulas - Couverture rigide

Livre 202 sur 202: Annals of Mathematics Studies

Kriz, Daniel

 
9780691216478: Supersingular p-adic L-functions, Maass-Shimura Operators and Waldspurger Formulas
Couverture rigide
ISBN 10 : 0691216479 ISBN 13 : 9780691216478
Editeur : Princeton University Press, 2021

Synopsis

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.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

À propos de l?auteur

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

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Princeton University Press
Date d'édition
2021
Langue
anglais
ISBN 10 
0691216479
ISBN 13 
9780691216478
Reliure
Relié
Nombre de pages
280
Coordonnées du fabricant
non disponible
Personne responsable
non disponible

Autres éditions populaires du même titre

9780691216461: Supersingular P-adic L-functions, Maass-shimura Operators and Waldspurger Formulas

Edition présentée

ISBN 10 :  0691216460 ISBN 13 :  9780691216461
Editeur : Princeton University Press, 2021
Couverture souple