4 citations · 6 across the 10 of their papers we have counts for
11 papers · 1 filter
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…