English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In a series of papers in the 1960s Shimura studied analytic families of abelian varieties with fixed polarization, endomorphism, and level structure. The isomorphism classes of abelian varieties in such a family are in one-to-one correspondence with the points of D/Y, where D is a symmetric domain and T is a discontinuous group of transformations of D. Shimura constructed a fibre system (V, W) where the base V is analytically isomorphic to D/T, the fibres are the abelian varieties in the family, and V and W are quasi-projective varieties. The fibre A over the generic point of V is an abelian variety defined over the function field K of V. The main result of this announcement is that, under certain conditions on the endomorphism algebra structure, the group of points of A defined over K is finite. Using completely different techniques, Shioda [8] proved this result in the case in which D is the complex upper half-plane and T is a congruence subgroup of SL»2(Z). The results in this note are an extension of part of the author's Ph.D. thesis [9]. Details will appear elsewhere. I would like to express my sincere thanks to my thesis advisor, Professor Goro Shimura.

Finiteness of Mordell-Weil groups of generic Abelian varieties