Decomposing Jacobians of curves with extra automorphisms
In this paper we generalize the deformation theory of representations of a profinite group developed by Schlessinger and Mazur to deformations of objects of the derived category of bounded complexes of pseudocompact modules for such a group. We show that such objects have versal deformations under certain natural conditions, and we find a sufficient condition for these versal deformations to be universal. Moreover, we consider applications to deforming Galois cohomology classes and the étale hypercohomology...
Soit un entier . Pour un nombre premier on note l’extension maximale non ramifiée de . Supposons que divise exactement . Alors, en utilisant les travaux de Carayol et la théorie du corps de classes local, on détermine une extension de sur laquelle la jacobienne de la courbe modulaire de admet une réduction semi-stable, puis on donne une estimation de son degré.
In [22], the authors proved an explicit formula for the arithmetic intersection number on the Siegel moduli space of abelian surfaces, under some assumptions on the quartic CM field . These intersection numbers allow one to compute the denominators of Igusa class polynomials, which has important applications to the construction of genus curves for use in cryptography. One of the main tools in the proof was a previous result of the authors [21] generalizing the singular moduli formula of Gross...
We give a parametrization of curves C of genus 2 with a maximal isotropic (ℤ/3)² in J[3], where J is the Jacobian variety of C, and develop the theory required to perform descent via (3,3)-isogeny. We apply this to several examples, where it is shown that non-reducible Jacobians have non-trivial 3-part of the Tate-Shafarevich group.