109 citations · 693 across the 41 of their papers we have counts for
42 papers · 1 filter
Ultra-Kolyvagin systems and non-ordinary Selmer groups
David Loeffler, Sarah Livia Zerbes
We develop a machine for bounding Selmer groups of Galois representations via Euler systems in "non-ordinary" settings, using Pottharst's definition of Selmer groups via Robba-ring…
Poles of p-adic Asai L-functions and distinguished representations
David Loeffler, Sarah Livia Zerbes
We give a criterion in terms of p-adic Asai L-functions for a cuspidal automorphic representation of GL(2) over a real quadratic field to be a distinguished representation, providi…
A universal Euler system for GSp(4)
David Loeffler, Sarah Livia Zerbes
In our earlier work with Christopher Skinner (J. Eur. Math. Soc 24 (2022), no. 2; DOI 10.4171/JEMS/1124; Arxiv 1706.00201), we constructed Euler systems for the 4-dimensional spin…
Asai-Flach classes, p-adic L-functions and the Bloch-Kato conjecture for GO(4)
Giada Grossi, David Loeffler, Sarah Livia Zerbes
We prove the Bloch-Kato conjecture for critical values of Asai L-functions of p-ordinary Hilbert modular forms over quadratic fields (with p split); and one inclusion in the Iwasaw…
An Euler system for the adjoint of a modular form
David Loeffler, Sarah Livia Zerbes
We construct an Euler system for the adjoint Galois representation of a modular form, using motivic cohomology classes arising from Hilbert modular surfaces. We use this Euler syst…
Asai-Flach classes and p-adic L-functions
Giada Grossi, David Loeffler, Sarah Livia Zerbes
We prove a formula for the Bloch-Kato logarithm of the bottom class in the Asai-Flach Euler system associated to a quadratic Hilbert modular form. We show that this can be expresse…
P-adic Asai L-functions for quadratic Hilbert eigenforms
Giada Grossi, David Loeffler, Sarah Livia Zerbes
We construct p-adic Asai L-functions for cuspidal automorphic representations of GL2 / F, where F is a real quadratic field in which p splits. Our method relies on higher Hida theo…
Plectic structures in p-adic de Rham cohomology
David Loeffler, Sarah Livia Zerbes
Given a Hilbert modular form for a totally real field , and a prime split completely in , the -eigenspace in -adic de Rham cohomology of the Hilbert modular variety…
On the Birch-Swinnerton-Dyer conjecture for modular abelian surfaces
David Loeffler, Sarah Livia Zerbes
Let be a modular abelian surface over which either has trivial geometric endomorphism ring, or arises as the restriction of scalars of an elliptic curve over an imaginary q…
Spherical varieties and p-adic families of cohomology classes
David Loeffler, Rob Rockwood, Sarah Livia Zerbes
We prove a "twist-compatibility" result for p-adic families of cohomology classes associated to symmetric spaces. This shows that a single family of classes (lying in a finitely-ge…
On p-adic regulators for GSp(4) x GL(2) and GSp(4) x GL(2) x GL(2)
David Loeffler, Sarah Livia Zerbes
We compute the images of motivic cohomology classes for GSp(4) x GL(2) and GSp(4) x GL(2) x GL(2) under the syntomic regulator, and relate them to non-critical values of p-adic L-f…
P-adic L-functions and diagonal cycles for GSp(4) x GL(2) x GL(2)
David Loeffler, Sarah Livia Zerbes
We develop a (largely conjectural) theory of p-adic L-functions interpolating square roots of central L-values for automorphic forms on GSp(4) x GL(2) x GL(2), and a relation betwe…
An Euler system for GU(2, 1)
David Loeffler, Christopher Skinner, Sarah Livia Zerbes
We construct an Euler system associated to regular algebraic, essentially conjugate self-dual cuspidal automorphic representations of GL(3) over imaginary quadratic fields, using t…
Iwasawa theory for quadratic Hilbert modular forms
David Loeffler, Sarah Livia Zerbes
We study the Iwasawa main conjecture for quadratic Hilbert modular forms over the p-cyclotomic tower. Using an Euler system in the cohomology of Siegel modular varieties, we prove…
On the Bloch--Kato conjecture for the symmetric cube
David Loeffler, Sarah Livia Zerbes
We prove one inclusion of the Iwasawa Main Conjecture, and the Bloch-Kato conjecture in analytic rank 0, for the symmetric cube of a level 1 modular form.
On the Bloch-Kato conjecture for GSp(4)
David Loeffler, Sarah Livia Zerbes
We prove an explicit reciprocity law for the Euler system attached to the spin motive of a genus 2 Siegel modular form. As consequences, we obtain one inclusion of the Iwasawa Main…
Higher Hida theory and p-adic L-functions for GSp(4)
David Loeffler, Vincent Pilloni, Christopher Skinner +1
We use the "higher Hida theory" recently introduced by the second author to p-adically interpolate periods of non-holomorphic automorphic forms for GSp(4), contributing to coherent…
Vologodsky integration on curves with semi-stable reduction
Amnon Besser, Sarah Livia Zerbes
We prove that the Vologodsky integral of a mermorphic one-form on a curve over a -adic field with semi-stable reduction restrict to Coleman integrals on the rigid subdomains red…
Euler systems with local conditions
David Loeffler, Sarah Livia Zerbes
Euler systems are certain compatible families of cohomology classes, which play a key role in studying the arithmetic of Galois representations. We briefly survey the known Euler s…
Euler systems for GSp(4)
David Loeffler, Chris Skinner, Sarah Livia Zerbes
We construct an Euler system for Galois representations associated to cohomological cuspidal automorphic representations of the group GSp(4), using the pushforwards of Eisenstein c…
Syntomic regulators of Asai--Flach classes
David Loeffler, Christopher Skinner, Sarah Livia Zerbes
In this paper, we derive a formula for the p-adic syntomic regulators of Asai--Flach classes. These are cohomology classes forming an Euler system associated to a Hilbert modular f…
Euler systems for Hilbert modular surfaces
Antonio Lei, David Loeffler, Sarah Livia Zerbes
We construct an Euler system -- a compatible family of global cohomology classes -- for the Galois representations appearing in the geometry of Hilbert modular surfaces. If a conje…
Iwasawa theory for the symmetric square of a modular form
David Loeffler, Sarah Livia Zerbes
We construct a compatible family of global cohomology classes (an Euler system) for the symmetric square of a modular form, and apply this to bounding Selmer groups of the symmetri…
On the asymptotic growth of Bloch-Kato-Shafarevich-Tate groups of modular forms over cyclotomic extensions
Antonio Lei, David Loeffler, Sarah Zerbes
We study the asymptotic behaviour of the Bloch-Kato-Shafarevich-Tate group of a modular form f over the cyclotomic Zp-extension of Q under the assumption that f is non-ordinary at…