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math.NT2022
Motivic local systems on curves and Maeda's conjecture
Yeuk Hay Joshua Lam
We show that only finitely many complex genus two curves and four punctured spheres admit rank two local systems of geometric origin, and moreover each carries finitely many. This…
math.NT2022
Boundedness of trace fields of rank two local systems
Yeuk Hay Joshua Lam
Let be a fixed prime number, and a power of . For any curve over and any local system on it, we have a number field generated by the traces of Frobenii at…
math.NT2022
Lifts of supersingular abelian varieties with small Mumford-Tate groups
Yeuk Hay Joshua Lam, Abhishek Oswal
We investigate to what extent an abelian variety over a finite field can be lifted to one in characteristic zero with small Mumford-Tate group. We prove that supersingular abelian…