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20172026
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math.NT2026

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

Matthew Bisatt, Lorenzo Furio, Davide Lombardo

Let be an elliptic curve whose mod Galois image is contained in the normaliser of a non-split Cartan. We classify the possible -adic images of 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

Matthew Bisatt

Let be a hyperelliptic curve with an affine model of the form . We explicitly determine the root number of the Jacobian of , with particular focus on t…

math.NT2019

Tame torsion, the tame inverse Galois problem, and endomorphisms

Matthew Bisatt

Fix a positive integer and rational prime . We prove the existence of a genus curve such that the mod 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

Frobenius elements in Galois representations with SL_n image

Matthew Bisatt

Suppose we have a elliptic curve over a number field whose mod representation has image isomorphic to . We present a method to determine Frobenius elements…