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Abelian Surfaces over totally real fields are potentially modular
| File | Description | Size | Format | |
|---|---|---|---|---|
 Boxer2021_Article_AbelianSurfacesOverTotallyReal (1).pdf | Published version | 3.62 MB | Adobe PDF | View/Open |
| Title: | Abelian Surfaces over totally real fields are potentially modular |
| Authors: | Boxer, G Calegari, F Gee, T Pilloni, V |
| Item Type: | Journal Article |
| Abstract: | We show that abelian surfaces (and consequently curves of genus 2) over totally real fields are potentially modular. As a consequence, we obtain the expected meromorphic continuation and functional equations of their Hasse–Weil zeta functions. We furthermore show the modularity of infinitely many abelian surfaces A over Q with EndCA = Z. We also deduce modularity and potential modularity results for genus one curves over (not necessarily CM) quadratic extensions of totally real fields. |
| Issue Date: | 29-Nov-2021 |
| Date of Acceptance: | 27-Oct-2021 |
| URI: | http://hdl.handle.net/10044/1/92990 |
| DOI: | 10.1007/s10240-021-00128-2 |
| ISSN: | 0073-8301 |
| Publisher: | Springer |
| Start Page: | 153 |
| End Page: | 501 |
| Journal / Book Title: | Publications mathématiques de l'IHÉS |
| Volume: | 134 |
| Copyright Statement: | © 2021 The Author(s). This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. |
| Sponsor/Funder: | Commission of the European Communities The Leverhulme Trust Engineering & Physical Science Research Council (EPSRC) The Royal Society |
| Funder's Grant Number: | FP7-ERC-StG-2012-306326 LH.PZ.GEE.2012 EP/L025485/1 WM150076 |
| Keywords: | 0101 Pure Mathematics General Mathematics |
| Publication Status: | Published |
| Online Publication Date: | 2021-11-29 |
| Appears in Collections: | Pure Mathematics Faculty of Natural Sciences Mathematics |
This item is licensed under a Creative Commons License
