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math.NT2024
Congruences of modular forms and modularity of Tate-Shafarevich classes
Matteo Tamiozzo
We prove, under suitable assumptions, that -torsion Tate-Shafarevich classes for elliptic curves over the rationals are visible in quotients of Jacobians of modular curves, as p…
math.NT2021
On the étale cohomology of Hilbert modular varieties with torsion coefficients
Ana Caraiani, Matteo Tamiozzo
We study the étale cohomology of Hilbert modular varieties, building on the methods introduced for unitary Shimura varieties in [CS17, CS19]. We obtain the analogous vanishing theo…
math.NT2019
On the Bloch-Kato conjecture for Hilbert modular forms
Matteo Tamiozzo
The aim of this paper is to prove inequalities towards instances of the Bloch-Kato conjecture for Hilbert modular forms of parallel weight two, when the order of vanishing of the $…