Matthew Bisatt

activity

20172026

most citedTame torsion, the tame inverse Galois problem, and endomorphisms

2 citations · 3 across the 8 of their papers we have counts for

collaborators

10 papers

math.NT2026

Explicit p-adic Hodge theory for elliptic curves and non-split Cartan images

Matthew Bisatt, Lorenzo Furio, Davide Lombardo

Let $E / Q_{p}$ be an elliptic curve whose mod $p$ Galois image is contained in the normaliser of a non-split Cartan. We classify the possible $p$ -adic images of $E$ using too…

math.NT2023

Conductors of twisted Weil--Deligne representations

Matthew Bisatt, Ross Paterson

We study the behaviour of conductors of L-functions associated to certain Weil--Deligne representations under twisting. For each global field K we prove a sharp upper bound for the…

math.NT2021

Root number of the Jacobian of $y^{2} = x^{p} + a$

Matthew Bisatt

Let $C / Q$ be a hyperelliptic curve with an affine model of the form $y^{2} = x^{p} + a$ . We explicitly determine the root number of the Jacobian of $C$ , with particular focus on t…

math.NT2020

A user's guide to the local arithmetic of hyperelliptic curves

Alex J. Best, L. Alexander Betts, Matthew Bisatt +8

A new approach has been recently developed to study the arithmetic of hyperelliptic curves $y^{2} = f (x)$ over local fields of odd residue characteristic via combinatorial data associa…

math.NT2019

Tame torsion and the tame inverse Galois problem

Matthew Bisatt, Tim Dokchitser

Fix a positive integer $g$ and a squarefree integer $m$ . We prove the existence of a genus $g$ curve $C / Q$ such that the mod $m$ representation of its Jacobian is tame. Th…

math.NT2019★ 2 cited

Tame torsion, the tame inverse Galois problem, and endomorphisms

Matthew Bisatt

Fix a positive integer $g$ and rational prime $p$ . We prove the existence of a genus $g$ curve $C / Q$ such that the mod $p$ representation of its Jacobian is tame by imposi…

math.NT2019

Clusters, inertia, and root numbers

Matthew Bisatt

In a recent paper of Dokchitser--Dokchitser--Maistret--Morgan, the authors introduced the concept of a cluster picture associated to a hyperelliptic curve from which they are able…

math.NT2017

Explicit root numbers of abelian varieties

Matthew Bisatt

The Birch and Swinnerton-Dyer conjecture predicts that the parity of the algebraic rank of an abelian variety over a global field should be controlled by the expected sign of the f…

math.NT2017★ 1 cited

On the Birch--Swinnerton-Dyer conjecture and Schur indices

Matthew Bisatt, Vladimir Dokchitser

For every odd prime $p$ , we exhibit families of irreducible Artin representations $τ$ with the property that for every elliptic curve $E$ the order of the zero of the twisted $L$ -f…

math.NT2017

Frobenius elements in Galois representations with SL_n image

Matthew Bisatt

Suppose we have a elliptic curve over a number field whose mod $l$ representation has image isomorphic to $S L_{2} (F_{l})$ . We present a method to determine Frobenius elements…

Explicit p-adic Hodge theory for elliptic curves and non-split Cartan images

Conductors of twisted Weil--Deligne representations

Root number of the Jacobian of y2=xp+a

A user's guide to the local arithmetic of hyperelliptic curves

Tame torsion and the tame inverse Galois problem

Tame torsion, the tame inverse Galois problem, and endomorphisms

Clusters, inertia, and root numbers

Explicit root numbers of abelian varieties

On the Birch--Swinnerton-Dyer conjecture and Schur indices

Frobenius elements in Galois representations with SL_n image

Root number of the Jacobian of $y^{2} = x^{p} + a$