92 citations · 177 across the 15 of their papers we have counts for
19 papers
On a local-global principle for quadratic twists of abelian varieties
Francesc Fité
Let and be abelian varieties defined over a number field of dimension . For , we show that the following local-global principle holds: and a…
Sato-Tate groups of abelian threefolds
Francesc Fité, Kiran S. Kedlaya, Andrew V. Sutherland
Given an abelian variety over a number field, its Sato-Tate group is a compact Lie group which conjecturally controls the distribution of Euler factors of the L-function of the abe…
Computing L-Polynomials of Picard curves from Cartier-Manin matrices
Sualeh Asif, Francesc Fité, Dylan Pentland
We study the sequence of zeta functions of a generic Picard curve defined over at primes of good reduction for . We define a degree 9 po…
Ordinary primes for some varieties with extra endomorphisms
Francesc Fité
Let A be an abelian variety defined over a number field and of dimension g. When g<3, by the recent work of Sawin, we know the exact (nonzero) value of the density of the set of pr…
Effective Sato-Tate conjecture for abelian varieties and applications
Alina Bucur, Francesc Fité, Kiran S. Kedlaya
From the generalized Riemann hypothesis for motivic L-functions, we derive an effective version of the Sato-Tate conjecture for an abelian variety A defined over a number field k w…
Arithmetic invariants from Sato--Tate moments
Edgar Costa, Francesc Fité, Andrew V. Sutherland
We give some arithmetic-geometric interpretations of the moments M_2[a_1], M_1[a_2], and M_1[s_2] of the Sato-Tate group of an abelian variety A defined over a number field by rela…
Tate module tensor decompositions and the Sato-Tate conjecture for certain abelian varieties potentially of -type
Francesc Fité, Xavier Guitart
We introduce a tensor decomposition of the -adic Tate module of an abelian variety defined over a number field which is geometrically isotypic. If is potentially…
Endomorphism algebras of geometrically split abelian surfaces over
Francesc Fité, Xavier Guitart
We determine the set of geometric endomorphism algebras of geometrically split abelian surfaces defined over . In particular we find that this set has cardinality 92. T…
On the Hilbert eigenvariety at exotic and CM classical weight 1 points
Adel Betina, Shaunak V. Deo, Francesc Fité
Let be a totally real number field and let be a classical cuspidal -regular Hilbert modular eigenform over of parallel weight . Let be the point on the -ad…
On the rank and the convergence rate towards the Sato-Tate measure
Francesc Fité, Xavier Guitart
Let be an abelian variety defined over a number field and let denote its Sato-Tate group. Under the assumption of certain standard conjectures on -functions attached to…
Fields of definition of elliptic -curves and the realizability of all genus 2 Sato--Tate groups over a number field
Francesc Fité, Xavier Guitart
Let be an abelian variety of dimension that is isogenous over to , where is an elliptic curve. If does not have comple…
Sato-Tate groups of y^2=x^8+c and y^2=x^7-cx
Francesc Fité, Andrew V. Sutherland
We consider the distribution of normalized Frobenius traces for two families of genus 3 hyperelliptic curves over Q that have large automorphism groups: y^2=x^8+c and y^2=x^7-cx wi…
Equidistribution, L-functions, and Sato-Tate groups
Francesc Fité
In this expository note, we present an approach to the generalization of Serre of the Sato-Tate Conjecture. Most of its content is taken from Serre's original references. However,…
Frobenius distribution for quotients of Fermat curves of prime exponent
Francesc Fité, Josep González, Joan-Carles Lario
Let C denote the Fermat curve over Q of prime exponent l. The Jacobian Jac(C) of C splits over Q as the product of Jacobians Jac(C_k), 0< k < l-1, where C_k are curves obtained as…
Sato-Tate groups of some weight 3 motives
Francesc Fité, Kiran S. Kedlaya, Andrew V. Sutherland
We establish the group-theoretic classification of Sato-Tate groups of self-dual motives of weight 3 with rational coefficients and Hodge numbers h^{3,0} = h^{2,1} = h^{1,2} = h^{0…
Sato-Tate distributions of twists of y^2=x^5-x and y^2=x^6+1
Francesc Fité, Andrew V. Sutherland
We determine the limiting distribution of the normalized Euler factors of an abelian surface A defined over a number field k when A is isogenous to the square of an elliptic curve…
Sato-Tate distributions and Galois endomorphism modules in genus 2
Francesc Fité, Kiran S. Kedlaya, Victor Rotger +1
For an abelian surface A over a number field k, we study the limiting distribution of the normalized Euler factors of the L-function of A. This distribution is expected to correspo…
The twisting representation of the -function of a curve
Francesc Fité, Joan-C. Lario
Let C be a smooth projective curve defined over a number field and let C' be a twist of C. In this article we relate the l-adic representations attached to the l-adic Tate modules…
Artin representations attached to pairs of isogenous abelian varieties
Francesc Fité
Given a pair of abelian varieties defined over a number field k and isogenous over a finite Galois extension L/k, we define a rational Artin representation of the group Gal(L/k) th…