Giada Grossi

collaborators

6 papers

math.NT2026

Higher Hida theory for Hilbert modular varieties in the totally split case

Giada Grossi

We study $p$ -adic properties of the coherent cohomology of some automorphic sheaves on the Hilbert modular variety $X$ for a totally real field $F$ in the case where the prime $p$ …

math.NT2026

Non-vanishing of Kolyvagin systems and Iwasawa theory

Ashay Burungale, Francesc Castella, Giada Grossi +1

Let $E / Q$ be an elliptic curve and $p$ an odd prime. In 1991 Kolyvagin conjectured that the system of cohomology classes for torsion quotients of the $p$ -adic Tate module…

math.NT2026

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…

math.NT2025

Mazur's main conjecture at Eisenstein primes

Francesc Castella, Giada Grossi, Christopher Skinner

Let $E / Q$ be an elliptic curve, let $p > 2$ be a prime of good reduction for $E$ , and assume that $E$ admits a rational $p$ -isogeny with kernel $F_{p} (I ¨ )$ . In this p…

math.NT2025

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…

math.NT2025

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…