Supersingular p-adic L-functions, Maass-Shimura Operators and Waldspurger Formulas : : (AMS-212) / / Daniel Kriz.
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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Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2021] ©2021 |
Year of Publication: | 2021 |
Language: | English |
Series: | Annals of Mathematics Studies ;
405 |
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Kriz, Daniel, author. aut http://id.loc.gov/vocabulary/relators/aut Supersingular p-adic L-functions, Maass-Shimura Operators and Waldspurger Formulas : (AMS-212) / Daniel Kriz. Princeton, NJ : Princeton University Press, [2021] ©2021 1 online resource (280 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Annals of Mathematics Studies ; 405 Frontmatter -- Contents -- Preface -- Acknowledgments -- 1 Introduction -- 2 Preliminaries: Generalities -- 3 Preliminaries: Geometry of the infinite-level modular curve -- 4 The fundamental de Rham periods -- 5 The p-adic Maass-Shimura operator -- 6 P-adic analysis of the p-adic Maass-Shimura operators -- 7 Bounding periods at supersingular CM points -- 8 Supersingular Rankin-Selberg p-adic L-functions -- 9 The p-adic Waldspurger formula -- Bibliography -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 01. Dez 2022) L-functions. Number theory. p-adic analysis. MATHEMATICS / Number Theory. bisacsh Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2021 9783110739121 https://doi.org/10.1515/9780691225739?locatt=mode:legacy https://www.degruyter.com/isbn/9780691225739 Cover https://www.degruyter.com/document/cover/isbn/9780691225739/original |
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English |
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Kriz, Daniel, Kriz, Daniel, |
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Kriz, Daniel, Kriz, Daniel, Supersingular p-adic L-functions, Maass-Shimura Operators and Waldspurger Formulas : (AMS-212) / Annals of Mathematics Studies ; Frontmatter -- Contents -- Preface -- Acknowledgments -- 1 Introduction -- 2 Preliminaries: Generalities -- 3 Preliminaries: Geometry of the infinite-level modular curve -- 4 The fundamental de Rham periods -- 5 The p-adic Maass-Shimura operator -- 6 P-adic analysis of the p-adic Maass-Shimura operators -- 7 Bounding periods at supersingular CM points -- 8 Supersingular Rankin-Selberg p-adic L-functions -- 9 The p-adic Waldspurger formula -- Bibliography -- Index |
author_facet |
Kriz, Daniel, Kriz, Daniel, |
author_variant |
d k dk d k dk |
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VerfasserIn VerfasserIn |
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Kriz, Daniel, |
title |
Supersingular p-adic L-functions, Maass-Shimura Operators and Waldspurger Formulas : (AMS-212) / |
title_sub |
(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_auth |
Supersingular p-adic L-functions, Maass-Shimura Operators and Waldspurger Formulas : (AMS-212) / |
title_alt |
Frontmatter -- Contents -- Preface -- Acknowledgments -- 1 Introduction -- 2 Preliminaries: Generalities -- 3 Preliminaries: Geometry of the infinite-level modular curve -- 4 The fundamental de Rham periods -- 5 The p-adic Maass-Shimura operator -- 6 P-adic analysis of the p-adic Maass-Shimura operators -- 7 Bounding periods at supersingular CM points -- 8 Supersingular Rankin-Selberg p-adic L-functions -- 9 The p-adic Waldspurger formula -- Bibliography -- Index |
title_new |
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) / |
series |
Annals of Mathematics Studies ; |
series2 |
Annals of Mathematics Studies ; |
publisher |
Princeton University Press, |
publishDate |
2021 |
physical |
1 online resource (280 p.) |
contents |
Frontmatter -- Contents -- Preface -- Acknowledgments -- 1 Introduction -- 2 Preliminaries: Generalities -- 3 Preliminaries: Geometry of the infinite-level modular curve -- 4 The fundamental de Rham periods -- 5 The p-adic Maass-Shimura operator -- 6 P-adic analysis of the p-adic Maass-Shimura operators -- 7 Bounding periods at supersingular CM points -- 8 Supersingular Rankin-Selberg p-adic L-functions -- 9 The p-adic Waldspurger formula -- Bibliography -- Index |
isbn |
9780691225739 9783110739121 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA247 |
callnumber-sort |
QA 3247 K75 42021 |
url |
https://doi.org/10.1515/9780691225739?locatt=mode:legacy https://www.degruyter.com/isbn/9780691225739 https://www.degruyter.com/document/cover/isbn/9780691225739/original |
illustrated |
Not Illustrated |
doi_str_mv |
10.1515/9780691225739?locatt=mode:legacy |
oclc_num |
1302163393 |
work_keys_str_mv |
AT krizdaniel supersingularpadiclfunctionsmaassshimuraoperatorsandwaldspurgerformulasams212 |
status_str |
n |
ids_txt_mv |
(DE-B1597)589308 (OCoLC)1302163393 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2021 |
is_hierarchy_title |
Supersingular p-adic L-functions, Maass-Shimura Operators and Waldspurger Formulas : (AMS-212) / |
container_title |
Title is part of eBook package: De Gruyter Princeton University Press Complete eBook-Package 2021 |
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