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Prof. Dr David Loeffler

  1. UniDistance Suisse
  2. Faculty of Mathematics and Computer Science
David Loeffler
Full Professor

Links

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David Loeffler joined UniDistance Suisse as Professor of Mathematics in November 2023. He was previously a professor at the University of Warwick in the UK. His research area is number theory, particularly focussing on modular forms, Galois representations, and L-functions. He is the leader of the ERC research project "Shimura varieties and the BSD conjecture" (2021-26). He is a member of the editorial boards of Trans. Amer. Math. Soc., Mathematika, and Publicacions Mathematiques.

Publications

Preprints

  • D. Loeffler and M. Stoll, Formalizing zeta and L-functions in Lean. (Arxiv)
  • D. Loeffler and S.L. Zerbes, Poles of p-adic Asai L-functions and distinguished representations. (Arxiv)
  • D. Loeffler and S.L. Zerbes, A universal Euler system for GSp(4). (Arxiv)
  • G. Grossi, D. Loeffler and S.L. Zerbes, Asai–Flach elements, p-adic L-functions and the Bloch–Kato conjecture for GO(4). (Arxiv)
  • Z. Hao and D. Loeffler, P-adic Rankin–Selberg L-functions in universal deformation families and functional equations. (Arxiv)
  • D. Loeffler and S.L. Zerbes, An Euler system for the adjoint of a modular form. (Arxiv)
  • G. Grossi, D. Loeffler and S.L. Zerbes, P-adic Asai L-functions for quadratic Hilbert eigenforms. (Arxiv)
  • D. Loeffler and C. Williams, P-adic L-functions for GL(3). (Arxiv)
  • D. Loeffler and S.L. Zerbes, On the Birch–Swinnerton-Dyer conjecture for modular abelian surfaces. (Arxiv)
  • A. Arlandini and D. Loeffler, On the factorisation of the p-adic Rankin–Selberg L-function in the supersingular case. (Arxiv)
  • D. Loeffler and S.L. Zerbes, Iwasawa theory for quadratic Hilbert modular forms. (Arxiv)
  • D. Loeffler and S.L. Zerbes, On the Bloch–Kato conjecture for GSp(4). (Arxiv)

Book project

Together with Sarah Zerbes, I am assembling a book Euler systems and the Bloch–Kato conjecture: the case of GSp(4) Ă—GL(2) and GSp(4) Ă— GL(2) Ă— GL(2). This includes the following papers of which I am an author:

  • D. Loeffler and S.L. Zerbes, P-adic L-functions and diagonal cycles for GSp(4) x GL(2) x GL(2). (Arxiv)
  • D. Loeffler and S.L. Zerbes, On p-adic regulators for GSp(4) x GL(2) and GSp(4) x GL(2) x GL(2). (Arxiv)
  • D. Loeffler and S.L. Zerbes, On the Bloch–Kato conjecture for GSp(4) x GL(2). (Arxiv)
  • D. Loeffler, On some zeta-integrals for unramified representations of GSp(4). (Arxiv)

This collection will also include the following papers by other authors:

  • C.-Y. Hsu, Z. Jin and R. Sakamoto, Euler systems for GSp(4) x GL(2). (Arxiv)

In press

  • D. Loeffler, R. Rockwood and S.L. Zerbes, Spherical varieties and p-adic families of cohomology classes. To appear in Elliptic curves and modular forms in arithmetic geometry – celebrating Massimo Bertolini's 60th birthday. (Arxiv)

2025

  • D. Loeffler and Ă“. Rivero, On p-adic L-functions for GSp4 x GL2. Pacific J. Math. 335 (2025), no. 2, 373–400. (Published version) (Arxiv) (SONAR)
  • D. Loeffler and S.L. Zerbes, Plectic structures in p-adic de Rham cohomology (in memory of Jan Nekovar). J. Number Theory 270 (2025), special issue for 2022 biennial conference, 238–259. (Published version) (Arxiv) (SONAR)

2024

  • D. Loeffler and Ă“. Rivero, Eisenstein degeneration of Euler systems. J. reine angew. Math. 814 (2024), 241–282. (Published version) (Arxiv) (SONAR)
  • D. Loeffler and Ă“. Rivero, Algebraicity of L-values for GSp(4) x GL(2) and GSp(4) x GL(2) x GL(2). Quarterly J Math 75 (2024), no. 2, 391–412. (Published version) (Arxiv) (SONAR)
  • D. Loeffler, On local zeta integrals for GSp(4) and GSp(4) x GL(2). New York J Math 30 (2024), 1–23. (Published version) (Arxiv) (SONAR)

2023

  • D. Loeffler and S.L. Zerbes, Euler systems and the Bloch–Kato conjecture for automorphic Galois representations (survey article). Proceedings of the 2022 International Congress of Mathematicians, volume III, 1918–1939. (Published version)
  • D. Loeffler and S.L. Zerbes, On the Bloch–Kato conjecture for the symmetric cube, J. Eur. Math. Soc. 25 (2023), no. 8, 3359–3363. (Published version) (Arxiv) (WRAP)
  • D. Loeffler, P-adic L-functions in universal deformation families, Ann. Math. QuĂ©bec 47 (2023), no. 1, 117–137 (special issue in honour of Bernadette Perrin-Riou). (Published version) (Arxiv) (WRAP)

2022

  • D. Loeffler, C. Skinner and S.L. Zerbes, Euler systems for GSp(4), J. Eur. Math. Soc. 24 (2022), no. 2, 669-733. (Published version) (Arxiv) (WRAP)
  • D. Loeffler, C. Skinner and S.L. Zerbes, An Euler system for GU(2, 1), Math. Annalen 382 (2022), 1091–1141. (Published version) (Arxiv) (WRAP)

2021

  • D. Loeffler, Spherical varieties and norm relations in Iwasawa theory, J. Th. Nombres Bordeaux 33 (2021), no. 3.2 (Iwasawa 2019 special issue), 1021–1043. (Published version) (Arxiv) (WRAP)
  • D. Loeffler, V. Pilloni, C. Skinner and S.L. Zerbes, Higher Hida theory and p-adic L-functions for GSp(4), Duke Math. J. 170 (2021), no. 18, 4033–4121. (Published version) (Arxiv) (WRAP)
  • D. Loeffler, Gross–Prasad periods for reducible representations, Forum Mathematicum 33 (2021), no. 5, 1169–1177. (Published version) (Arxiv) (WRAP)
  • D. Jetchev, D. Loeffler and S.L. Zerbes, Heegner points in Coleman families, Proc. London Math. Soc. 122 (2021), no. 1, 124–152. (Published version) (Arxiv) (WRAP)

2020

  • D. Loeffler, C. Skinner and S.L. Zerbes, Syntomic regulators of Asai–Flach classes. In Development of Iwasawa Theory – the Centennial of K. Iwasawa's Birth (M. Kurihara et al, eds), vol. 86 of Adv. Stud. Pure Math., Math. Soc. Japan, 2020, 595–638. (Published version) (Arxiv) (WRAP)
  • D. Loeffler and S.L. Zerbes, Euler systems with local conditions (expository article). In Development of Iwasawa Theory – the Centennial of K. Iwasawa's Birth (M. Kurihara et al, eds), vol. 86 of Adv. Stud. Pure Math., Math. Soc. Japan, 2020, 1–26. (Published version) (Arxiv) (WRAP)
  • D. Loeffler and C. Williams, P-adic Asai L-functions for Bianchi modular forms, Algebra & Number Theory 14 (2020), no. 7, 1669–1710. (Published version) (Arxiv) (WRAP)
  • G. Kings, D. Loeffler and S.L. Zerbes, Rankin–Eisenstein classes for modular forms, American J. Math. 142 (2020), no. 1, 79–138. ( Published version) (Arxiv) (WRAP)

2019

  • D. Loeffler and S.L. Zerbes, Iwasawa theory for the symmetric square of a modular form, J. Reine Angew. Math. 752 (2019), 179–210. (Published version) (Arxiv) (WRAP)
  • K. BĂĽyĂĽkboduk, A. Lei, D. Loeffler and G. Venkat, Iwasawa theory for Rankin–Selberg products of p-non-ordinary eigenforms, Algebra & Number Theory 13 (2019), no. 4, 901–941. (Published version) (Arxiv) (WRAP)
  • L. DembĂ©lĂ©, D. Loeffler and A. Pacetti, Non-paritious Hilbert modular forms, Math. Zeit. 292 (2019), no. 1, 361–385. ( Published version) (Arxiv) (WRAP)

2018

  • A. Lei, D. Loeffler and S.L. Zerbes, Euler systems for Hilbert modular surfaces, Forum Math. Sigma 6 (2018), e23. ( Published version) (Arxiv) (WRAP)
  • D. Loeffler, A note on p-adic Rankin–Selberg L-functions, Canad. Math. Bulletin 61 (2018), no. 3, 608–621. (Published version) (Arxiv) (WRAP)

2017

  • A. Lei, D. Loeffler and S.L. Zerbes, On the asymptotic growth of Bloch–Kato–Shafarevich–Tate groups of modular forms over cyclotomic extensions, Canad. J. Math. 69 (2017), no. 4, 826–850. (Published version) (Arxiv) (WRAP)
  • G. Kings, D. Loeffler and S.L. Zerbes, Rankin–Eisenstein classes and explicit reciprocity laws, Cambridge J. Math. 5 (2017), no. 1, 1–122. ( Published version) (Arxiv) (WRAP)
  • D. Loeffler, Images of adelic Galois representations for modular forms, Glasgow Math. J. 59 (2017), no. 1, 11—25. (Published version) (Arxiv) (WRAP)

2016

  • D. Loeffler and S.L. Zerbes, Rankin–Eisenstein classes in Coleman families, Res. Math. Sci 3 (2016), 29 (special issue in honour of Robert F. Coleman). ( Published version) (Arxiv) (WRAP)
  • A. Besser, D. Loeffler and S.L. Zerbes, Finite polynomial cohomology for general varieties, in P-adic Variation in Number Theory (Glenn Stevens' 60th birthday), Annales mathĂ©matiques du QuĂ©bec 40 (2016), no. 1, 203—220. (Published version) (Arxiv) (WRAP)

2015

  • A. Lei, D. Loeffler and S.L. Zerbes, Euler systems for modular forms over imaginary quadratic fields, Compos. Math. 151 (2015), no. 9, 1585—1625. (Published version) (Arxiv) (WRAP)
  • D. Loeffler, O. Venjakob and S.L. Zerbes, Local epsilon-isomorphisms, Kyoto J. Math. 55 (2015), no. 1, 63—127. (Published version) (Arxiv) (WRAP)

2014

  • D. Loeffler, P-adic integration on ray class groups and non-ordinary p-adic L-functions, in Iwasawa Theory 2012: State of the Art and Recent Advances (ed. T. Bouganis and O. Venjakob), vol. 7 of Contributions in Mathematical and Computational Sciences, Springer, 2014, 357—378. (Published version) (Arxiv) (WRAP)
  • D. Loeffler and S.L. Zerbes, Iwasawa theory and p-adic L-functions over Zp2-extensions, Int. J. Number Theory 10 (2014), no. 8, 2045—2095. (Published version) (Arxiv) (WRAP)
  • A. Lei, D. Loeffler and S.L. Zerbes, Euler systems for Rankin–Selberg convolutions of modular forms, Ann. of Math. 180 (2014), no. 2, 653—771. ( Published version) (Arxiv) (WRAP)
  • T. Hamilton and D. Loeffler, Congruence testing for odd subgroups of the modular group, LMS J. Comput. Math. 17 (2014), no. 1, 206—208. (Published version) (Arxiv) (WRAP)
  • D. Loeffler, Computing with algebraic automorphic forms (expository article), in Computations with Modular Forms: Proceedings of a Summer School and Conference, Heidelberg, August/September 2011 (ed. G. Böckle and G. Wiese), vol. 6 of Contributions in Mathematical and Computational Sciences, Springer, 2014, 47—68. (Published version) (link) (WRAP)

2013

  • A. Lei, D. Loeffler and S.L. Zerbes, Critical slope p-adic L-functions of CM modular forms, Israel J. Math. 198 (2013), no. 1, 261—282. ( Published version) (Arxiv) (WRAP)
  • D. Loeffler and S.L. Zerbes, Wach modules and critical slope p-adic L-functions, J. Reine Angew. Math. 679 (2013), 181—206. (Published version) (Arxiv) (WRAP)

2012

  • R. Hill and D. Loeffler, P-adic interpolation of metaplectic forms of cohomological type, Int. J. Number Theory 8 (2012), no. 7, 1—48. (Published version) (Arxiv) (WRAP)
  • D. Loeffler and J. Weinstein, On the computation of local components of a newform, Mathematics of Computation 81 (2012), 1179—1200. ( Published version) (Arxiv) (WRAP) — see also erratum (Mathematics of Computation 84 (2015), no. 291, 355—356).

2011

  • A. Lei, D. Loeffler and S.L. Zerbes, Coleman maps and the p-adic regulator, Algebra & Number Theory 5 (2011), no. 8, 1095–1131. ( Published version) (Arxiv) (WRAP)
  • D. Loeffler, Density of classical points in eigenvarieties, Mathematical Research Letters 18 (2011), no. 5, 983—990. ( Published version) (Arxiv) (WRAP)
  • R. Hill and D. Loeffler, Emerton's Jacquet functors for non-Borel parabolic subgroups, Documenta Math. 16 (2011), 1—31. ( Published version) (Arxiv) (WRAP)
  • D. Loeffler, Overconvergent algebraic automorphic forms, Proc. London Math. Soc. 102 (2011), no. 2, 193—228. (Published version) (Arxiv) (WRAP)
    • See also correction in Proc. London Math. Soc. 114 (2017), no. 1, 399--400.

2010

  • A. Lei, D. Loeffler and S.L. Zerbes, Wach modules and Iwasawa theory for modular forms, Asian J. Math. 14 (2010), no. 4, 475—528. ( Published version) (Arxiv) (WRAP)

2008

  • D. Loeffler, Explicit calculations of automorphic forms for definite unitary groups, LMS J. Comput. Math 11 (2008), 326—342. ( Published version) (Arxiv) (WRAP)

2007

  • D. Loeffler, Spectral expansions of overconvergent modular functions, Int. Math. Res. Not 2007, no. 16. (Published version) (Arxiv) (WRAP)

Not for publication

  • G. Kings, D. Loeffler and S.L. Zerbes, Rankin–Selberg Euler systems and p-adic interpolation, preprint. (Arxiv) This paper has been withdrawn, as there is a substantial gap in the arguments. It is replaced by the two papers "Rankin–Eisenstein classes for modular forms" and "Rankin–Eisenstein classes and explicit reciprocity laws" (see above.)

Research groups

Number theory

  • Peer-reviewed
    DOI
    On p-adic L-functions for GSp4Ă—GL2
    2025-05 | Journal of Mathematical Sciences Publishers
    Loeffler David // Rivero Salgado Óscar
    On p-adic L-functions for GSp4Ă—GL2
    DOI
    2025-05 | Journal of Mathematical Sciences Publishers
    Loeffler David // Rivero Salgado Óscar
    Peer-reviewed
  • Peer-reviewed
    DOI
    Eisenstein degeneration of Euler systems
    2024-08 | Journal of Walter de Gruyter GmbH
    Loeffler David // Rivero Salgado Óscar
    Eisenstein degeneration of Euler systems
    DOI
    2024-08 | Journal of Walter de Gruyter GmbH
    Loeffler David // Rivero Salgado Óscar
    Peer-reviewed
  • DOI
    Euler systems and the Bloch–Kato conjecture for automorphic Galois representations
    2023-12 | Journal of EMS Press
    Loeffler David // Sarah Livia Zerbes
    Euler systems and the Bloch–Kato conjecture for automorphic Galois representations
    DOI
    2023-12 | Journal of EMS Press
    Loeffler David // Sarah Livia Zerbes
  • Peer-reviewed
    DOI
    Plectic structures in p-adic de Rham cohomology
    2023-11 | Journal of Elsevier BV
    Loeffler David // Sarah Livia Zerbes
    Plectic structures in p-adic de Rham cohomology
    DOI
    2023-11 | Journal of Elsevier BV
    Loeffler David // Sarah Livia Zerbes
    Peer-reviewed
  • Peer-reviewed
    DOI
    On the Bloch–Kato conjecture for the symmetric cube
    2022-07 | Journal of European Mathematical Society - EMS - Publishing House GmbH
    Loeffler David // Sarah Livia Zerbes
    On the Bloch–Kato conjecture for the symmetric cube
    DOI
    2022-07 | Journal of European Mathematical Society - EMS - Publishing House GmbH
    Loeffler David // Sarah Livia Zerbes
    Peer-reviewed
  • Peer-reviewed
    DOI
    P-adic L-functions in universal deformation families
    2021-12 | Journal of Springer Science and Business Media LLC
    Loeffler David
    P-adic L-functions in universal deformation families
    DOI
    2021-12 | Journal of Springer Science and Business Media LLC
    Loeffler David
    Peer-reviewed
  • Peer-reviewed
    DOI
    Euler systems for GSp(4)
    2021-08 | Journal of European Mathematical Society - EMS - Publishing House GmbH
    Loeffler David // Sarah Livia Zerbes // Christopher Skinner
    Euler systems for GSp(4)
    DOI
    2021-08 | Journal of European Mathematical Society - EMS - Publishing House GmbH
    Loeffler David // Sarah Livia Zerbes // Christopher Skinner
    Peer-reviewed
  • Peer-reviewed
    DOI
    An Euler system for GU(2, 1)
    2021-07 | Journal of Springer Science and Business Media LLC
    Loeffler David // Sarah Livia Zerbes // Christopher Skinner
    An Euler system for GU(2, 1)
    DOI
    2021-07 | Journal of Springer Science and Business Media LLC
    Loeffler David // Sarah Livia Zerbes // Christopher Skinner
    Peer-reviewed

Teaching

M04 Linear Algebra I Bachelor of Science in Mathematics
Linear Algebra I Bachelor of Science in Mathematics
Linear Algebra I Bachelor of Science in Mathematics
M14 Number Theory Bachelor of Science in Mathematics
Number Theory Bachelor of Science in Mathematics
Number Theory Bachelor of Science in Mathematics
M18 Seminar on special topics Bachelor of Science in Mathematics
Seminar on special topics Bachelor of Science in Mathematics
Seminar on special topics Bachelor of Science in Mathematics

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