1 citations · 1 across the 11 of their papers we have counts for
12 papers
-adic Galois representations of elliptic curves over the rationals via Kummer descent
Santiago Arango-Piñeros, David Zureick-Brown
We show that the two modular curves of level and genus left open by the work of Rouse, Sutherland and Zureick-Brown, and of Furio and Lombardo, have no non-CM rational poi…
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…
Bounds for the relative class number problem for function fields
Santiago Arango-Piñeros, María Chara, Asimina S. Hamakiotes +2
We establish bounds on a finite separable extension of function fields in terms of the relative class number, thus reducing the problem of classifying extensions with a fixed relat…
Galois groups of low dimensional abelian varieties over finite fields
Santiago Arango-Piñeros, Sam Frengley, Sameera Vemulapalli
We consider three isogeny invariants of abelian varieties over finite fields: the Galois group, Newton polygon, and the angle rank. Motivated by work of Dupuy, Kedlaya, and Zureick…
Frobenius distributions of low dimensional abelian varieties over finite fields
Santiago Arango-Piñeros, Deewang Bhamidipati, Soumya Sankar
Given a -dimensional abelian variety over a finite field , the Weil conjectures imply that the normalized Frobenius eigenvalues generate a multiplicative group…
Mertens' theorem for Chebotarev sets
Santiago Arango-Piñeros, Daniel Keliher, Christopher Keyes
We generalize Mertens' product theorem to Chebotarev sets of prime ideals in Galois extensions of number fields. Using work of Rosen, we extend an argument of Williams from cycloto…
Global Field Totients
Santiago Arango-Piñeros, Juan Diego Rojas
Using a remainder theorem for valuations of a field, we give a new perspective on the norm function of a global field. We define the Euler totient function of a global field and re…