9 papers
On -adic solubility of
Santiago Arango-Piñeros, Christopher Keyes, Andrew Kobin
We study -adic solubility of generalized Fermat equations for positive integers . For all but finitely many primes , the probability of…
Counting number fields of fixed degree by their smallest defining polynomial
Santiago Arango-Piñeros, Fabian Gundlach, Robert J. Lemke Oliver +5
When do two irreducible polynomials with integer coefficients define the same number field? One can define an action of on the space of polynom…
Counting primitive integral solutions to spherical generalized Fermat equations
Santiago Arango-Piñeros
A solution to a generalized Fermat equation \[ Ax^a + By^b + Cz^c = 0, \] is called \emph{primitive} if . By work of Beukers…
Fermat descent
Santiago Arango-Piñeros
Descent theory (a modern formulation of Fermat's classical method of infinite descent) is a powerful tool in arithmetic geometry. In this article, we reinterpret descent theory thr…
Galois groups of simple abelian varieties over finite fields and exceptional Tate classes
Santiago Arango-Piñeros, Sam Frengley, Sameera Vemulapalli
We prove new cases of the Tate conjecture for abelian varieties over finite fields, extending previous results of Dupuy--Kedlaya--Zureick-Brown, Lenstra--Zarhin, Tankeev, and Zarhi…
Counting 5-isogenies of elliptic curves over
Santiago Arango-Piñeros, Changho Han, Oana Padurariu +1
We show that the number of -isogenies of elliptic curves defined over with naive height bounded by is asymptotic to for some e…