Dylan Pentland

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20202025

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math.NT2025

Syntomification and crystalline local systems

Dylan Pentland

Let $p$ be a prime, and let $X$ be a smooth $p$ -adic formal scheme over $Spf O_{K}$ where $K / Q_{p}$ is a finite extension. We show that reflexive s…

math.NT2021

Extensions of mod p representations of division algebras over non-Archimedean local fields

Andrew Keisling, Dylan Pentland

Let $F$ be a local field over $Q_{p}$ or $F_{p} ((t))$ , and let $D$ be a central simple division algebra over $F$ of degree $d$ . In the $p$ -adic case, we assume $p>de+…

math.NT2020

Computing L-Polynomials of Picard curves from Cartier-Manin matrices

Sualeh Asif, Francesc Fité, Dylan Pentland

We study the sequence of zeta functions $Z (C_{p}, T)$ of a generic Picard curve $C : y^{3} = f (x)$ defined over $Q$ at primes $p$ of good reduction for $C$ . We define a degree 9 po…