Euler systems and the conjectures of Birch and Swinnerton-Dyer, Bloch and Kato

Project Information

BSD

Grant agreement ID: 682152

DOI 10.3030/682152

Project closed

EC signature date 11 July 2016

Start date 1 September 2016

End date 31 August 2022

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost € 1 428 588,00

EU contribution € 1 428 588,00

Coordinated by

UNIVERSITAT POLITECNICA DE CATALUNYA
Spain

Publications

Peer reviewed articles (46)

Variation of anticyclotomic Iwasawa invariants in Hida families

Author(s): Francesc Castella, Chan-Ho Kim, Matteo Longo
Published in: Algebra and Number Theory, Issue 11, 2017, Page(s) 2339-2368, ISSN 1937-0652
Publisher: Mathematical Sciences Publishers

Endomorphism algebras of geometrically splitabelian surfaces over ℚ

Author(s): Francesc Fité, Xavier Guitart
Published in: Algebra & Number Theory, Issue 14/6, 2020, Page(s) 1399-1421, ISSN 1937-0652
Publisher: Mathematical Sciences Publishers
DOI: 10.2140/ant.2020.14.1399

On the $p$-adic periods of the modular curve $X(\Gamma _0(p) \cap \Gamma (2))$

Author(s): Adel Betina, Emmanuel Lecouturier
Published in: Transactions of the American Mathematical Society, Issue 371/1, 2019, Page(s) 413-429, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/7236

The exceptional zero phenomenon for elliptic units

Author(s): Óscar Rivero
Published in: Revista Matemática Iberoamericana, 2020, ISSN 0213-2230
Publisher: Universidad Autonoma de Madrid
DOI: 10.4171/rmi/1229

p-adic families of d-th Shintani liftings

Author(s): Daniele Casazza, Carlos de Vera-Piquero
Published in: Annales mathématiques du Québec, 2019, ISSN 2195-4763
Publisher: Springer

Special values of triple-product p-adic L-functions and non-crystalline diagonal classes

Author(s): Francesca Gatti, Xavier Guitart, Marc Masdeu, Victor Rotger
Published in: Journal de Théorie des Nombres de Bordeaux, Issue 3, 2022, Page(s) 809-834, ISSN 1246-7405
Publisher: Universite de Bordeaux III

Del Pezzo surfaces over finite fields and their Frobenius traces

Author(s): Barinder Banwait, Francesc Fité, Daniel Loughran
Published in: Mathematical Proceedings of the Cambridge Philosophical Society, Issue 167, 2019, Page(s) 35-60, ISSN 0305-0041
Publisher: Cambridge University Press

A quaternionic construction of p-adic singular moduli

Author(s): Xavier Guitart, Marc Masdeu, Xavier Xarles
Published in: Research in the Mathematical Sciences, Issue 8, 2022, ISSN 2522-0144
Publisher: Springer

Class groups and local indecomposability for non-CM forms

Author(s): Francesc Castella, Carl Wang-Erickson, Haruzo Hida
Published in: Journal of the European Mathematical Society, Issue 24, 2022, Page(s) 1103-1160, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House
DOI: 10.4171/jems/1107

Congruences formulas for Legendre modular polynomials

Author(s): Adel Betina, Emmanuel Lecouturier
Published in: Journal of Number Theory, Issue 188, 2018, Page(s) 71-87, ISSN 0022-314X
Publisher: Academic Press

Finite slope Triple Product p-adic L-functions over totally real fields

Author(s): Santiago Molina
Published in: Journal of Number Theory, Issue 223, 2021, Page(s) 267-306, ISSN 0022-314X
Publisher: Academic Press

Plectic p-adic invariants

Author(s): Michele Fornea; Xavier Guitart; Marc Masdeu
Published in: Advances in Mathematics, 2022, ISSN 0001-8708
Publisher: Academic Press

Pullbacks of Saito-Kurokawa Lifts and a Central Value Formula for Degree 6 L-Series

Author(s): Aprameyo Pal, Carlos de Vera-Piquero
Published in: Documenta Mathematica, Issue 24, 2019, Page(s) 1935-2036, ISSN 1431-0635
Publisher: Deutsche Mathematiker-Vereinigung
DOI: 10.25537/dm.2019v24.1935-2036

Derived Beilinson-Flach elements and the arithmetic of the adjoint of a modular form

Author(s): Óscar Rivero, Victor Rotger
Published in: Journal of the European Mathematical Society, Issue 23, 2021, Page(s) 2299-2335, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House

p-adic families of diagonal cycles

Author(s): Henri Darmon; Victor Rotger
Published in: Astérisque, Issue 434, 2022, ISSN 0303-1179
Publisher: Societe Mathematique de France
DOI: 10.48550/arXiv.2207.01314

On the L‐invariant of the adjoint of a weight one modular form

Author(s): Marti Roset, Victor Rotger, Vinayak Vatsal
Published in: Journal of the London Mathematical Society, 2021, ISSN 0024-6107
Publisher: Oxford University Press
DOI: 10.1112/jlms.12428

Generalized Kato classes and exceptional zero conjectures

Author(s): Óscar Rivero
Published in: Indiana University Mathematics Journal, Issue 71, 2022, Page(s) 649-684, ISSN 0022-2518
Publisher: Indiana University Press

On the analogue of Mazur-Tate type conjectures in the Rankin-Selberg setting

Author(s): Antonio Cauchi, Antonio Lei
Published in: Publicacions Matematiques, Issue 66, 2022, Page(s) 571-630, ISSN 0210-2978
Publisher: Universitat Autonoma de Barcelona

Extremal p-adic L-functions

Author(s): Santiago Molina
Published in: Mathematics, Issue 9, 2021, ISSN 2227-7390
Publisher: MDPI

Fields of definition of elliptic $k$-curves and the realizability of all genus 2 Sato–Tate groups over a number field

Author(s): Francesc Fité, Xavier Guitart
Published in: Transactions of the American Mathematical Society, Issue 370/7, 2018, Page(s) 4623-4659, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/7074

The derived Hecke algebra for dihedral weight one forms

Author(s): Henri Darmon; Michael Harris; Victor Rotger; Akshay Venkatesh
Published in: Michigan Mathematical Journal, Issue 72, 2022, Page(s) 145-207, ISSN 0026-2285
Publisher: University Of Michigan, Department of Mathematics

On the Elliptic Stark Conjecture in higher weight

Author(s): Francesca Gatti; Xavier Guitart
Published in: Publicacions Matemàtiques, Issue 6, 2020, ISSN 0210-2978
Publisher: Universitat Autònoma de Barcelona
DOI: 10.5565/publmat6422009

Overconvergent Eichler–Shimura isomorphisms for quaternionic modular forms over ℚ

Author(s): Daniel Barrera Salazar; Shan Gao
Published in: International Journal of Number Theory, 2017, Page(s) 2487-2504, ISSN 1793-0421
Publisher: World Scientific Publishing Co
DOI: 10.1142/s1793042117501494

p-adic heights of Heegner points and Beilinson-Flach classes

Author(s): Francesc Castella
Published in: Journal of the London Mathematical Society, Issue 96/1, 2017, Page(s) 156-180, ISSN 0024-6107
Publisher: Oxford University Press
DOI: 10.1112/jlms.12058

On the failure of Gorensteinness at weight 1 Eisenstein points of the eigencurve

Author(s): Adel Betina, Mladen Dimitrov, Alice Pozzi
Published in: American Journal of Mathematics, Issue 144, 2018, Page(s) 227-265, ISSN 0002-9327
Publisher: The Johns Hopkins University Press

On the Hilbert eigenvariety at exotic and CM classical weight 1 points

Author(s): Adel Betina, Shaunak V. Deo, Francesc Fité
Published in: Mathematische Zeitschrift, 2021, ISSN 0025-5874
Publisher: Springer Verlag
DOI: 10.1007/s00209-020-02626-1

On the p-adic variation of Heegner points

Author(s): Francesc Castella
Published in: J. Inst. Math. Jussieu, Issue 19, 2020, Page(s) 2127-2164, ISSN 1474-7480
Publisher: Cambridge University Press

Anticyclotomic $p$-adic $L$-functions and the exceptional zero phenomenon

Author(s): Santiago Molina
Published in: Transactions of the American Mathematical Society, 2019, Page(s) 1, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/7646

Ramification of the Eigencurve at Classical RM Points

Author(s): Adel Betina
Published in: Canadian Journal of Mathematics, 2019, Page(s) 1-32, ISSN 0008-414X
Publisher: Canadian Mathematical Society
DOI: 10.4153/cjm-2018-029-4

On the $p$-part of the Birch–Swinnerton-Dyer formula for multiplicative primes

Author(s): Francesc Castella
Published in: Cambridge Journal of Mathematics, Issue 6/1, 2018, Page(s) 1-23, ISSN 2168-0930
Publisher: International Press
DOI: 10.4310/cjm.2018.v6.n1.a1

Exceptional zeros and $\mathcal {L}$-invariants of Bianchi modular forms

Author(s): Daniel Barrera Salazar, Chris Williams
Published in: Transactions of the American Mathematical Society, 2019, Page(s) 1, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/7436

On the Rank and the Convergence Rate Toward the Sato–Tate Measure

Author(s): Francesc Fité, Xavier Guitart
Published in: International Mathematics Research Notices, 2017, ISSN 1073-7928
Publisher: Oxford University Press
DOI: 10.1093/imrn/rnx234

An automorphic approach to Darmon points

Author(s): X. Guitart, M. Masdeu, S. Molina
Published in: Indiana University Mathematics Journal, 2019, ISSN 0022-2518
Publisher: Indiana University Press

Sato–Tate distributions of twists of the Fermat and the Klein quartics

Author(s): Francesc Fité, Elisa Lorenzo García, Andrew V. Sutherland
Published in: Research in the Mathematical Sciences, Issue 5/4, 2018, ISSN 2522-0144
Publisher: Springer
DOI: 10.1007/s40687-018-0162-0

On the elliptic Stark conjecture at primes of multiplicative reduction

Author(s): Daniele Casazza, Victor Rotger
Published in: Indiana University Mathematics Journal, Issue 68, 2019, Page(s) 1233-1253, ISSN 0022-2518
Publisher: Indiana University Press

Periods of Modular GL 2 -type Abelian Varieties and p -adic Integration

Author(s): Xavier Guitart, Marc Masdeu
Published in: Experimental Mathematics, Issue 27/3, 2017, Page(s) 344-361, ISSN 1058-6458
Publisher: A K Peters Ltd.
DOI: 10.1080/10586458.2017.1284624

Families of Picard modular forms and an application to the Bloch–Kato conjecture

Author(s): Valentin Hernandez
Published in: Compositio Mathematica, Issue 155/7, 2019, Page(s) 1327-1401, ISSN 0010-437X
Publisher: London Mathematical Society
DOI: 10.1112/s0010437x1900736x

Beilinson–Flach elements, Stark units and -adic iterated integrals

Author(s): Óscar Rivero, Victor Rotger
Published in: Forum Mathematicum, Issue 0/0, 2019, ISSN 0933-7741
Publisher: Walter de Gruyter GmbH & Co. KG
DOI: 10.1515/forum-2018-0281

Families of Bianchi modular symbols: critical base-change p-adic L-functions and p-adic Artin formalism

Author(s): Daniel Barrera Salazar, Chris Williams, Carl Wang-Erickson
Published in: Selecta Mathematica, Issue 82, 2021, Page(s) 1-45, ISSN 1022-1824
Publisher: Birkhauser Verlag

$p$-adic $L$-functions of Hilbert cusp forms and the trivial zero conjecture

Author(s): Barrera, Daniel; Dimitrov, Mladen; Jorza, Andrei
Published in: Journal of the European Mathematical Society, Issue 24, 2022, Page(s) 3439-3503, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House

Tate module tensor decompositions and the Sato-Tate conjecture for certain abelian varieties potentially of $\mathrm{GL}_2$-type

Author(s): Francesc Fite; Xavier Guitart
Published in: Mathematische Zeitschrift, Issue 3, 2022, Page(s) 2975-2995, ISSN 0025-5874
Publisher: Springer Verlag

p-adic L-functions for GL(2)

Author(s): Daniel Barrera Salazar, Christopher Williams
Published in: Canadian Journal of Mathematics, Issue 71, 2019, Page(s) 1019-1059, ISSN 0008-414X
Publisher: Canadian Mathematical Society

AUTOMORPHIC SL 2 ‐PERIODS AND THE SUBCONVEXITY PROBLEM FOR GL 2 × GL 3

Author(s): Aprameyo Pal, Carlos de Vera‐Piquero
Published in: Mathematika, Issue 66/4, 2020, Page(s) 855-899, ISSN 0025-5793
Publisher: University College London, Department of Mathematics
DOI: 10.1112/mtk.12047

Stark points and the Hida–Rankin p-adic L-function

Author(s): Daniele Casazza, Victor Rotger
Published in: The Ramanujan Journal, Issue 45/2, 2018, Page(s) 451-473, ISSN 1382-4090
Publisher: Kluwer Academic Publishers
DOI: 10.1007/s11139-016-9824-y

Stark-Heegner points and diagonal classes

Author(s): Henri Darmon, Victor Rotger
Published in: Astérisque, Issue 434, 2022, ISSN 0303-1179
Publisher: Societe Mathematique de France

Overconvergent cohomology of Hilbert modular varieties and $p$-adic $L$-functions

Author(s): Daniel Barrera Salazar
Published in: Ann. Inst. Fourier, 2018, Page(s) 2177-2213, ISSN 0373-0956
Publisher: Association des Annales de I'Institut Fourier
DOI: 10.5802/aif.3206

Other (17)

Cyclotomic derivatives of Beilinson--Flach classes and a p-adic Harris--Venkatesh conjecture

Author(s): Óscar Rivero, Victor Rotger
Published in: 2021
Publisher: Cornell University

Homotopy groups of spectra and p-adic L-functions over totally real number fields

Author(s): Guillem Sala
Published in: 2022
Publisher: Cornell University

On p-adic L-functions for GL2n in finite slope Shalika families

Author(s): Daniel Barrera; Mladen Dimitrov; Christopher Williams
Published in: 2021
Publisher: Cornell University

Algebraic cycles and functorial lifts from G2 to PGSp6

Author(s): Antonio Cauchi, Francesco Lemma, Joaquin Rodrigues Jacinto
Published in: 2022
Publisher: Cornell University

Exceptional zero formulas for anticyclotomic p-adic L-functions

Author(s): Victor Hernandez; Santiago Molina
Published in: 2021
Publisher: Cornell University

Sato-Tate groups of abelian threefolds

Author(s): Francesc Fité; Kiran Keldaya; Andrew Sutherland
Published in: 2021
Publisher: Cornell University

Plectic points and Hida-Rankin p-adic L-functions

Author(s): Victor Hernandez; Santiago Molina
Published in: 2022
Publisher: Cornell University

Motivic congruences and Sharifi's conjecture

Author(s): Óscar Rivero, Victor Rotger
Published in: 2021
Publisher: Cornell University

Kolyvagin classes versus non-cristalline diagonal classes

Author(s): Francesca Gatti, Victor Rotger
Published in: 2021
Publisher: Cornell University

Higher regulators of Siegel sixfolds and non-critical values of Spin L-functions

Author(s): Antonio Cauchi, Francesco Lemma, Joaquin Rodrigues Jacinto
Published in: 2022
Publisher: Cornell University

Waldspurger formulas in higher cohomology

Author(s): Santiago Molina
Published in: 2022
Publisher: Cornell University

Triple product p-adic L-functions for Shimura curves over totally real number fields

Author(s): Daniel Barrera Salazar, Santiago Molina
Published in: 2019
Publisher: Cornell University

Iwasasa theory for GL2xGL2 and diagonal cycles

Author(s): Raul Alonso; Francesc Castella; Oscar Rivero
Published in: 2021
Publisher: Cornell University

On Higher regulators of Siegel varieties

Author(s): Antonio Cauchi, Francesco Lemma, Joaquín Rodrigues Jacinto
Published in: 2020
Publisher: Cornell University

A truncated Siegel-Weil formula and Borcherds forms

Author(s): Armando Gutierrez
Published in: 2022
Publisher: Cornell University

On the Iwasawa main conjectures for modular forms at non-ordinary primes

Author(s): Francesc Castella, Mirela Ciperiani, Christopher Skinner, Florian Sprung
Published in: 2018
Publisher: Cornell University

Effective Sato-Tate conjecture for abelian varieties and applications

Author(s): Alina Bucur, Francesc Fité, Kiran S. Kedlaya
Published in: 2020
Publisher: Cornell University

Book chapters (1)

First Order p-Adic Deformations of Weight One Newforms

Author(s): Henri Darmon, Alan Lauder, Victor Rotger
Published in: L-Functions and Automorphic Forms, Issue 10, 2017, Page(s) 39-80, ISBN 978-3-319-69711-6
Publisher: Springer International Publishing
DOI: 10.1007/978-3-319-69712-3_4