Description: A groundbreaking contribution to number theory that unifies classical and modern resultsThis 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.
Price: 110 GBP
Location: Gloucester
End Time: 2025-01-28T18:21:28.000Z
Shipping Cost: 41.3 GBP
Product Images
Item Specifics
Return postage will be paid by: Buyer
Returns Accepted: Returns Accepted
After receiving the item, your buyer should cancel the purchase within: 60 days
Return policy details:
EAN: 9780691216478
UPC: 9780691216478
ISBN: 9780691216478
MPN: N/A
Item Length: 23.6 cm
Item Weight: 0.57 kg
Number of Pages: 280 Pages
Publication Name: Supersingular P-Adic L-Functions, Maass-Shimura Operators and Waldspurger Formulas: (Ams-212)
Language: English
Publisher: Princeton University Press
Item Height: 235 mm
Subject: Mathematics
Publication Year: 2021
Type: Textbook
Author: Daniel Kriz
Item Width: 156 mm
Series: Annals of Mathematics Studies
Format: Hardcover
