Supersingular p-adic L-functions, Maass-Shimura Operators and Waldspurger Formulas: (AMS-212)
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...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Princeton, Oxford
Princeton University Press
[2022]
|
| Series: | Annals of Mathematics Studies
Band 212 |
| Subjects: | |
| Online Access: | DE-1043 DE-1046 DE-858 DE-859 DE-860 DE-739 Volltext |
| Summary: | 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 |
| Item Description: | Bandzählung laut die Webseite : 402 |
| Physical Description: | 1 Online-Ressource (xv, 280 Seiten) |
| ISBN: | 9780691225739 |
| DOI: | 10.1515/9780691225739 |
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| 520 | |a 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 | ||
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| index_date | 2024-07-03T19:19:55Z |
| indexdate | 2025-02-19T17:33:36Z |
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| isbn | 9780691225739 |
| language | English |
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| spelling | Kriz, Daniel J. 1992- (DE-588)1247640930 aut Supersingular p-adic L-functions, Maass-Shimura Operators and Waldspurger Formulas (AMS-212) Daniel Kriz Princeton, Oxford Princeton University Press [2022] © 2021 1 Online-Ressource (xv, 280 Seiten) txt rdacontent c rdamedia cr rdacarrier Annals of Mathematics Studies Band 212 Bandzählung laut die Webseite : 402 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 MATHEMATICS / Number Theory bisacsh L-functions Number theory p-adic analysis Erscheint auch als Druck-Ausgabe, Paperback 978-0-691-21646-1 Erscheint auch als Druck-Ausgabe, Paperback 0-691-21646-0 Erscheint auch als Druck-Ausgabe, Hardcover 978-0-691-21647-8 Erscheint auch als Druck-Ausgabe, Hardcover 0-691-21647-9 Annals of Mathematics Studies Band 212 (DE-604)BV040389493 212 https://doi.org/10.1515/9780691225739 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Kriz, Daniel J. 1992- Supersingular p-adic L-functions, Maass-Shimura Operators and Waldspurger Formulas (AMS-212) Annals of Mathematics Studies MATHEMATICS / Number Theory bisacsh L-functions Number theory p-adic analysis |
| title | Supersingular p-adic L-functions, Maass-Shimura Operators and Waldspurger Formulas (AMS-212) |
| title_auth | Supersingular p-adic L-functions, Maass-Shimura Operators and Waldspurger Formulas (AMS-212) |
| title_exact_search | Supersingular p-adic L-functions, Maass-Shimura Operators and Waldspurger Formulas (AMS-212) |
| title_exact_search_txtP | Supersingular p-adic L-functions, Maass-Shimura Operators and Waldspurger Formulas (AMS-212) |
| title_full | Supersingular p-adic L-functions, Maass-Shimura Operators and Waldspurger Formulas (AMS-212) Daniel Kriz |
| title_fullStr | Supersingular p-adic L-functions, Maass-Shimura Operators and Waldspurger Formulas (AMS-212) Daniel Kriz |
| title_full_unstemmed | Supersingular p-adic L-functions, Maass-Shimura Operators and Waldspurger Formulas (AMS-212) Daniel Kriz |
| title_short | Supersingular p-adic L-functions, Maass-Shimura Operators and Waldspurger Formulas |
| title_sort | supersingular p adic l functions maass shimura operators and waldspurger formulas ams 212 |
| title_sub | (AMS-212) |
| topic | MATHEMATICS / Number Theory bisacsh L-functions Number theory p-adic analysis |
| topic_facet | MATHEMATICS / Number Theory L-functions Number theory p-adic analysis |
| url | https://doi.org/10.1515/9780691225739 |
| volume_link | (DE-604)BV040389493 |
| work_keys_str_mv | AT krizdanielj supersingularpadiclfunctionsmaassshimuraoperatorsandwaldspurgerformulasams212 |