Matthew Bisatt

activity

20172021

collaborators

4 papers

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.NT2019

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

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…

Root number of the Jacobian of y2=xp+a

Tame torsion, the tame inverse Galois problem, and endomorphisms

Clusters, inertia, and root numbers

Frobenius elements in Galois representations with SL_n image

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