Shimura varieties and the Birch--Swinnerton-Dyer conjecture

Project Information

ShimBSD

Grant agreement ID: 101001051

DOI

10.3030/101001051

EC signature date 24 March 2021

Start date 1 May 2021

End date 31 August 2026

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 739 143,00

EU contribution

€ 1 739 143,00

Coordinated by

FERNUNI SCHWEIZ
Switzerland

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Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Peer reviewed articles (14)

<i>p</i>-adic Rankin–Selberg <i>L</i>-functions in universal deformation families and functional equations

Author(s): Zeping Hao, David Loeffler
Published in: Forum Mathematicum, 2025, ISSN 0933-7741
Publisher: Walter de Gruyter GmbH & Co. KG
DOI: 10.1515/forum-2024-0497

On Greenberg–Benois $\mathcal {L}$-invariants and Fontaine–Mazur $\mathcal {L}$-invariants

Author(s): Ju-Feng Wu
Published in: Canadian Mathematical Bulletin, Issue 67, 2025, Page(s) 1141-1160, ISSN 0008-4395
Publisher: Canadian Mathematical Society
DOI: 10.4153/s0008439524000638

Finite polynomial cohomology with coefficients

Author(s): Ting-Han Huang, Ju-Feng Wu
Published in: Rendiconti del Seminario Matematico della Università di Padova, Issue (Published online), 2024, ISSN 0041-8994
Publisher: Casa Editrice Dott. Antonio Milani
DOI: 10.4171/rsmup/173

On p-adic L-functions for GSp4×GL2

Author(s): David Loeffler, Óscar Rivero
Published in: Pacific Journal of Mathematics, Issue 335, 2025, Page(s) 373-400, ISSN 0030-8730
Publisher: University of California at Berkeley
DOI: 10.2140/pjm.2025.335.373

Eisenstein degeneration of Euler systems

Author(s): David Loeffler, Oscar Rivero Salgado
Published in: Journal für die reine und angewandte Mathematik (Crelles Journal), Issue 2024, 2024, Page(s) 241-282, ISSN 0075-4102
Publisher: Walter de Gruyter GmbH & Co. KG
DOI: 10.1515/crelle-2024-0057

On local zeta-integrals for GSp(4) and GSp(4) x GL(2)

Author(s): Loeffler, David
Published in: New York J Math, Issue Vol. 30, 2024, Page(s) 1–23, ISSN 1076-9803
Publisher: Electronic Journals Project
DOI: 10.48550/arxiv.2011.15106

On -adic adjoint -functions for Bianchi cuspforms: The -split case

Author(s): Pak-Hin Lee, Ju-Feng Wu
Published in: Trans. Amer. Math. Soc, Issue Published online, print version to appear, 2025, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/9388

On integral aspects of Asai periods and Euler systems for Res_<i>E</i>/ℚGL₂

Author(s): Alexandros Groutides
Published in: Forum Mathematicum, Issue (Published online, print version to appear), 2025, ISSN 0933-7741
Publisher: Walter de Gruyter GmbH & Co. KG
DOI: 10.1515/forum-2024-0458

Euler Product Asymptotics for L-functions of Elliptic Curves

Author(s): Arshay Sheth
Published in: International Mathematics Research Notices, Issue 2025, 2025, ISSN 1073-7928
Publisher: Oxford University Press
DOI: 10.1093/imrn/rnaf214

Plectic structures in p-adic de Rham cohomology

Author(s): David Loeffler; Sarah Livia Zerbes
Published in: Journal of Number Theory, Issue (published online, print version to appear), 2023, ISSN 0022-314X
Publisher: Academic Press
DOI: 10.1016/j.jnt.2023.10.016

Control theorems for Hilbert modular varieties

Author(s): Arshay Sheth
Published in: Canadian Mathematical Bulletin, Issue (Published online, print version to appear), 2025, Page(s) 1-20, ISSN 0008-4395
Publisher: Canadian Mathematical Society
DOI: 10.4153/s0008439524000791

Control theorems for Hilbert modular varieties

Author(s): Arshay Sheth
Published in: Canadian Mathematical Bulletin, Issue 68, 2025, Page(s) 530-549, ISSN 0008-4395
Publisher: Canadian Mathematical Society
DOI: 10.4153/s0008439524000791

Algebraicity of L-values for GSp4×GL2 and GSp4×GL2×GL2

Author(s): Loeffler, David; Rivero, Óscar
Published in: Quarterly J Math, Issue Vol. 75 no. 2, 2024, Page(s) 391-412, ISSN 0033-5606
Publisher: Oxford University Press
DOI: 10.1093/qmath/haae016

Euler Products at the centre and applications to Chebyshev's bias

Author(s): Arshay Sheth
Published in: Math. Proc. Cambridge Phil. Soc., Issue (to appear), 2025, ISSN 0305-0041
Publisher: Cambridge University Press
DOI: 10.48550/arxiv.2405.01512

Other (14)

An Euler system for the adjoint of a modular form

Author(s): David Loeffler, Sarah Livia Zerbes
Published in: [PREPRINT], 2023
Publisher: Mathematics arXiv
DOI: 10.48550/arxiv.2312.04665

Integral structures in smooth GL2(Qp)-representations and zeta integrals

Author(s): Groutides, Alexandros
Published in: [PREPRINT], 2024
Publisher: Mathematics ArXiv
DOI: 10.48550/arxiv.2401.10870

P-adic Asai L-functions for quadratic Hilbert eigenforms

Author(s): Grossi, Giada; Loeffler, David; Zerbes, Sarah Livia
Published in: [PREPRINT], 2023
Publisher: Mathematics ArXiv
DOI: 10.48550/arxiv.2307.07004

A universal Euler system for GSp(4)

Author(s): David Loeffler, Sarah Livia Zerbes
Published in: [PREPRINT], 2024
Publisher: Mathematics ArXiv
DOI: 10.48550/arxiv.2411.12576

On the p-ranks of class groups of certain Galois extensions

Author(s): Ufuoma Asarhasa, Rusiru Gambheera, Debanjana Kundu, Enrique Nunez Lon-wo, Arshay Sheth
Published in: [PREPRINT], 2024
Publisher: Mathematics ArXiv
DOI: 10.48550/arxiv.2408.04481

On Rankin-Selberg integral structures and Euler systems for GL2×GL2

Author(s): Alexandros Groutides
Published in: [PREPRINT], 2024
Publisher: Mathematics ArXiv
DOI: 10.48550/arxiv.2407.01377

Moduli spaces of untwisted wild Riemann surfaces

Author(s): Douçot, Jean; Rembado, Gabriele; Tamiozzo, Matteo
Published in: [PREPRINT], 2024
Publisher: Mathematics ArXiv
DOI: 10.48550/arxiv.2403.18505

A p-adic Gross-Zagier formula for twisted triple product p-adic L-functions attached to finite slope families

Author(s): Ting-Han Huang, Ananyo Kazi
Published in: [PREPRINT], 2025
Publisher: Mathematics arXiv
DOI: 10.48550/arxiv.2501.17474

On the Bloch--Kato conjecture for GSp(4) x GL(2)

Author(s): Loeffler, David; Zerbes, Sarah Livia
Published in: [PREPRINT], 2021
Publisher: Mathematics ArXiv
DOI: 10.48550/arxiv.2106.14511

Asai-Flach classes, p-adic L-functions and the Bloch-Kato conjecture for GO(4)

Author(s): Giada Grossi, David Loeffler, Sarah Livia Zerbes
Published in: [PREPRINT], 2024
Publisher: Mathematics ArXiv
DOI: 10.48550/arxiv.2407.17055

On the Birch-Swinnerton-Dyer conjecture for modular abelian surfaces

Author(s): Loeffler, David; Zerbes, Sarah Livia
Published in: [PREPRINT], 2021
Publisher: Mathematics ArXiv
DOI: 10.48550/arxiv.2110.13102

Spherical varieties and p-adic families of cohomology classes

Author(s): Loeffler, David; Rockwood, Robert; Zerbes, Sarah Livia
Published in: [PREPRINT], 2021
Publisher: Mathematics ArXiv
DOI: 10.48550/arxiv.2106.16082

On some zeta-integrals for unramified representations of GSp(4)

Author(s): Loeffler, David
Published in: [PREPRINT], 2021
Publisher: Mathematics ArXiv
DOI: 10.48550/arxiv.2106.16076

On the Bloch-Kato conjecture for GSp(4)

Author(s): David Loeffler, Sarah Livia Zerbes
Published in: [PREPRINT], 2024
Publisher: Mathematics ArXiv
DOI: 10.48550/arxiv.2003.05960