4 citations · 6 across the 10 of their papers we have counts for
11 papers
Fields with no everywhere good abelian varieties
Armand Brumer, Kenneth Kramer
We extend methods of Fontaine, Abrashkin and Schoof to obtain criteria determining number fields K over which no non-zero abelian variety with everywhere good reduction exists. As…
Prosaic Abelian Varieties Bad at One Prime
Armand Brumer, Kenneth Kramer
We say that an abelian variety of dimension is {\em prosaic} if it is semistable, with good reduction at 2 and its points of order generate a -extension…
Computing nonsurjective primes associated to Galois representations of genus curves
Barinder S. Banwait, Armand Brumer, Hyun Jong Kim +4
For a genus curve over whose Jacobian admits only trivial geometric endomorphisms, Serre's open image theorem for abelian surfaces asserts that there are o…
Hyperelliptic -curves of prime conductor
Armand Brumer, Kenneth Kramer
An abelian threefold of prime conductor is favorable if its 2-division field is an -extension over with ramification index…
On the paramodularity of typical abelian surfaces (and reduction of G-covariant bilinear forms)
Armand Brumer, Ariel Pacetti, Cris Poor +3
Generalizing the method of Faltings-Serre, we rigorously verify that certain abelian surfaces without extra endomorphisms are paramodular. To compute the required Hecke eigenvalues…
Large 2-adic Galois image and non-existence of certain abelian surfaces over Q
Armand Brumer, Kenneth Kramer
Motivated by our arithmetic applications, we required some tools that might be of independent interest. Let be an absolutely irreducible group scheme of rank ove…