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Higher Chow cycles on Abelian surfaces and a non-Archimedean analogue of the Hodge- ${\mathcal{D}}$ -conjecture

  • Ramesh Sreekantan (a1)

Abstract

We construct new indecomposable elements in the higher Chow group $CH^2(A,1)$ of a principally polarized Abelian surface over a $p$ -adic local field, which generalize an element constructed by Collino [Griffiths’ infinitesimal invariant and higher K-theory on hyperelliptic Jacobians, J. Algebraic Geom. 6 (1997), 393–415]. These elements are constructed using a generalization, due to Birkenhake and Wilhelm [Humbert surfaces and the Kummer plane, Trans. Amer. Math. Soc. 355 (2003), 1819–1841 (electronic)], of a classical construction of Humbert. They can be used to prove a non-Archimedean analogue of the Hodge- ${\mathcal{D}}$ -conjecture – namely, the surjectivity of the boundary map in the localization sequence – in the case where the Abelian surface has good and ordinary reduction.

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References

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Higher Chow cycles on Abelian surfaces and a non-Archimedean analogue of the Hodge- ${\mathcal{D}}$ -conjecture

  • Ramesh Sreekantan (a1)

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