6 papers · 1 filter
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…
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…
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…
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…
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…
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…