Decomposition theorems for arithmetic cycles

Abstract: We will describe some decomposition theorems for cycles over polarized varieties in both local and global settings under some conjectures of Lefschetz type. In local settings, our decomposition theorems are essentially non-archimedean analogues of ``harmonic forms" on Kahler manifolds. As an application, we will define a notion of ``admissible pairings" of algebraic cycles which is a simultaneous generalization of Beilinson--Bloch height pairing, and the local intersection pairings developed by Arakelov, Faltings, and Gillet--Soule on Kahler manifolds. In global setting, our decomposition theorems provide canonical splittings of some canonical filtrations, including canonical liftings of homological cycles to algebraic cycles.

algebraic geometrynumber theory

Audience: researchers in the topic

( paper | slides )

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MIT number theory seminar

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