Degrees of polarizations on an abelian surface with real multiplication
Abstract
Description
Let F be a real quadratic field, and let R be an order in F. Suppose given a polarized abelian surface (A,λ) defined over a number field k with a symmetric action of R defined over k. This paper considers varying A within the k-isogeny class of A to reduce the degree of λand the conductor of R. It is proved, in particular, that there is a k-isogenous principally polarized abelian surface with an action of the full ring of integers of F when F has class number 1 and the degree of λand the conductor of R are odd and coprime.
14 pages; LaTeX2e source; to be published in Bulletin of the LMS
14 pages; LaTeX2e source; to be published in Bulletin of the LMS