Prof. Dr David Loeffler

Publications

Preprints

• 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) ×GL(2) and GSp(4) × GL(2) × 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 and M. Stoll, Formalizing zeta and L-functions in Lean. To appear in Annals of Formalized Mathematics. (Arxiv)
• 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 Ó. 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 Ó. Rivero, Eisenstein degeneration of Euler systems. J. reine angew. Math. 814 (2024), 241–282. (Published version) (Arxiv) (SONAR)
• D. Loeffler and Ó. 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. Québec 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. Büyükboduk, 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. Dembélé, 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 mathématiques du Québec 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 Z_p²-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.)