Laboratoire de Mathématiques Blaise Pascal

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19932026

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11 papers · 2 filters

math.NT2024

Wieferich primes for Drinfeld modules

Xavier Caruso, Quentin Gazda, Alexis Lucas

The aim of this paper is to discuss the notion of Wieferich primes in the context of Drinfeld modules. Our main result is a surprising connection between the proprety of a monic ir…

math.NT2024

The convergence Newton polygon of a $p$ -adic differential equation IV : controlling graphs

Jérôme Poineau, Andrea Pulita

In our previous works we proved a finiteness property of the radii of convergence functions associated with a vector bundle with connection on $p$ -adic analytic curves. We showed t…

math.NT2024

A Jacquet-Langlands functor for $p$ -adic locally analytic representations

Gabriel Dospinescu, Juan Esteban Rodríguez Camargo

We study the locally analytic theory of infinite level local Shimura varieties. As a main result, we prove that in the case of a duality of local Shimura varieties, the locally ana…

math.NT2024

Hirzebruch-Zagier cycles in $p$ -adic families and adjoint $L$ -values

Antonio Cauchi, Marc-Hubert Nicole, Giovanni Rosso

Let $E / F$ be a quadratic extension of totally real number fields. We show that the generalized Hirzebruch-Zagier cycles arising from the associated Hilbert modular varieties can be…

math.NT2024

Conductor exponents for families of hyperelliptic curves

Martin Azon, Mar Curcó-Iranzo, Maleeha Khawaja +2

We compute the conductor exponents at odd places using the machinery of cluster pictures of curves for three infinite families of hyperelliptic curves. These are families of Frey h…

math.NT2024

Abelian surfaces over $F_{q} (t)$ with large Tate-Shafarevich groups

Martin Azon

We produce an explicit sequence $(S_{a})_{a \geq 1}$ of abelian surfaces over the rational function field $F_{q} (t)$ whose Tate-Shafarevich groups are finite and…

Wieferich primes for Drinfeld modules

The convergence Newton polygon of a p-adic differential equation IV : controlling graphs

A Jacquet-Langlands functor for p-adic locally analytic representations

Hirzebruch-Zagier cycles in p-adic families and adjoint L-values

Conductor exponents for families of hyperelliptic curves

Abelian surfaces over Fq​(t) with large Tate-Shafarevich groups

The convergence Newton polygon of a $p$ -adic differential equation IV : controlling graphs

A Jacquet-Langlands functor for $p$ -adic locally analytic representations

Hirzebruch-Zagier cycles in $p$ -adic families and adjoint $L$ -values

Abelian surfaces over $F_{q} (t)$ with large Tate-Shafarevich groups