Now showing items 1-11 of 11

• #### Abelian varieties with many endomorphisms and their absolutely simple factors ﻿

(2012)
Article
Restricted access - publisher's policy
We characterize the abelian varieties arising as absolutely simple factors of GL2-type varieties over a number field k. In order to obtain this result, we study a wider class of abelian varieties: the k-varieties ...
• #### Cropping Euler factors of modular L-functions ﻿

(2013-09)
Article
Open Access
According to the Birch and Swinnerton-Dyer conjectures, if A/Q is an abelian variety, then its L-function must capture a substantial part of the properties of A. The smallest number field L where A has all its endomorphisms ...
• #### Generalized Clifford-Severi inequality and the volume of irregular varieties ﻿

(2015-02-15)
Article
Open Access
We give a sharp lower bound for the self-intersection of a nef line bundle L on an irregular variety X in terms of its continuous global sections and the Albanese dimension of X, which we call the generalized Clifford-Severi ...
• #### Genus two curves with quaternionic multiplication and modular jacobian ﻿

(2007)
Article
Open Access
We describe a method to determine all the isomorphism classes of principal polarizations of the modular abelian surfaces $A_f$ with quaternionic multiplication attached to a normalized newform $f$ without complex ...
• #### Modular abelian varieties over number fields ﻿

(2014)
Article
Restricted access - publisher's policy
The main result of this paper is a characterization of the abelian varieties B=K defined over Galois number fields with the property that the L-function L(B=K; s) is a product of L-functions of non-CM newforms over Q for ...
• #### On the bicanonical map of irregular varieties ﻿

(2010-02)
Research report
Open Access
From the point of view of uniform bounds for the birationality of pluricanonical maps, irregular varieties of general type and maximal Albanese dimension behave similarly to curves. In fact Chen-Hacon showed that, at least ...
• #### On the modularity level of modular abelian varieties over number fields ﻿

(2010-07)
Article
Open Access
Let f be a weight two newform for Γ1(N) without complex multiplication. In this article we study the conductor of the absolutely simple factors B of the variety A f over certain number fields L. The strategy we follow ...
• #### On the Sato-Tate conjecture for non-generic abelian surfaces ﻿

(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.
• #### Riemann, funciones theta y variedades abelianas ﻿

(2008-04-02)
Audiovisual
Open Access
Se definirán las funciones theta de una variable y se explicará su relación con la teoría de funciones elípticas. Se dará una introducción a la teoría de formas modulares y a la relación entre la función theta y la función ...
• #### The Frobenius traces distribution for modular Abelian surfaces ﻿

(2014-02)
Article
Restricted access - publisher's policy
We prove that there exist at least 15 pairs of measures for which the two normalized Frobenius traces on modular Abelian surfaces are equidistributed. Under an assumption about stochastic independence, we prove that there ...
• #### Theta-duality in abelian varieties and the bicanonical map of irregular varieties ﻿

(Universitat Politècnica de Catalunya, 2010-05-18)
Doctoral thesis
Open Access
The first goal of this Thesis is to contribute to the study of principally polarized abelian varieties (ppav), especially to the Schottky and the Torelli problems. Ppav admit a duality theory analogous to that of projective ...