Abelian surfaces, Kummer surfaces and the non-Archimedean Hodge-D-conjecture

Details Abelian surfaces, Kummer surfaces and the non-Archimedean Hodge-D-conjecture Abelian surfaces, Kummer surfaces and the non-Archimedean Hodge-D-conjecture

2011-02-08

arxiv.org/abs/1102.1701v1

Mathematics

Number Theory

16 pages, 3 figures

Scientific paper

We construct new elements in the higher Chow group CH2(A,1) of a principally polarized Abelian surface over a non Archimedean local field, which generalize an element constructed by Collino. These elements are constructed using a generalization, due to Birkenhake and Wilhelm, of a classical construction of Humbert. They can be used to prove the non-Archimedean Hodge-D-conjecture - namely, the surjectivity of the boundary map in the localization sequence - in the case when the Abelian surface has good and ordinary reduction.

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