Now showing items 1-4 of 4

  • Del Pezzo surfaces over finite fields and their Frobenius traces 

    Banwait, Barinder; Fite Naya, Francesc; Loughran, Daniel (2019-07)
    Article
    Open Access
    Let S be a smooth cubic surface over a finite field q. It is known that #S( q) = 1 + aq + q2 for some a ¿ {-2, -1, 0, 1, 2, 3, 4, 5, 7}. Serre has asked which values of a can arise for a given q. Building on special cases ...
  • Fields of definition of elliptic k-curves and the realizability of all genus 2 sato–tate groups over a number field 

    Fite Naya, Francesc; Guitart Morales, Xavier (2018-07-01)
    Article
    Open Access
    Let A/Q be an abelian variety of dimension g = 1 that is isogenous over Q to Eg, where E is an elliptic curve. If E does not have complex multiplication (CM), by results of Ribet and Elkies concerning fields of definition ...
  • On the rank and the convergence rate toward the Sato-Tate measure 

    Fite Naya, Francesc; Guitart Morales, Xavier (2019-07-13)
    Article
    Open Access
    Let A be an abelian variety defined over a number field and let G denote its Sato–Tate group. Under the assumption of certain standard conjectures on L -functions attached to the irreducible representations of G, we study ...
  • On the Sato-Tate conjecture for non-generic abelian surfaces 

    Johansson, Christian; Fite Naya, Francesc (2017-01)
    Article
    Open Access
    We prove many non-generic cases of the Sato-Tate conjecture for abelian surfaces as formulated by Fité, Kedlaya, Rotger and Sutherland, using the potential automorphy theorems of Barnet-Lamb, Gee, Geraghty and Taylor.