ISSN:
1432-1785
Keywords:
Mathematics Subject Classification (1991):14H40, 11G10, 11F11
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract: Ribet [Ri] has generalized the conjecture of Shimura–Taniyama–Weil to abelian varieties defined over Q,giving rise to the study of abelian varieties of GL2-type. In this context, all curves over Q of genus one have Jacobian variety of GL2-type. Our aim in this paper is to begin with the analysis of which curves of genus 2 have Jacobian variety of GL2-type. To this end, we restrict our attention to curves with rational Rosenhain model and non-abelian automorphism group, and use the embedding of this group into the endomorphism algebra of its Jacobian variety to determine if it is of GL2-type.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002290050123
Permalink
