Heuristics based on the Sato–Tate conjecture and the Lang–Trotter philosophy suggest that
an abelian surface defined over a number field has infinitely many places of split reduction …

We describe an algorithm, based on the properties of the characteristic polynomials of
Frobenius, to compute $\operatorname {End} _ {\overline {K}}(A) $ when $ A $ is the …

Consider an absolutely simple abelian variety A defined over a number field K. For most
places v of K, we study how the reduction A v of A modulo v splits up into isogeny. Assuming …

Let A be an abelian variety of dimension g, defined over a number field K. Denote by NA the
norm of the conductor ideal of A. For each prime 𝖕 in K such that 𝖕 ł NA, denote by Ā𝖕 the …

This article is a survey of our work (joint with Davesh Maulik, Arul Shankar, and Salim
Tayou) on arithmetic intersection theory on GSpin Shimura varieties with applications to …

Split abelian surfaces over finite fieldsand reductions of genus-2 curves Page 1 Algebra &
Number Theory msp Volume 11 2017 No. 1 Split abelian surfaces over finite fields and …

Let $ A $ be a simple abelian variety over a number field $ k $ such that $\operatorname
{End}(A) $ is noncommutative. We show that $ A $ splits modulo all but finitely many primes …

Let $ A $ be an absolutely simple abelian surface defined over a number field $ K $ with a
commutative (geometric) endomorphism ring. Let $\pi_ {A,\text {split}}(x) $ denote the …

Let A be a g-dimensional abelian variety over Q whose adelic Galois representation has
open image in GSp 2 g Z ˆ. We investigate the Frobenius fields Q (π p)= End (A p)⊗ Q of the …

We study the special fibers of a certain class of absolutely simple abelian varieties over
number fields with endomorphism rings $\bz $ and possessing $ l $-adic monodromy …