Alladi Ramakrishnan Hall

Higher Chow cycles on Abelian Surfaces

Ramesh Sreekantan

ISI Bangalore

In this talk we use generalizations of beautiful classical geometric
constructions of Kummer and Humbert to construct new motivic cohomology
cycles on Abelian surfaces and K3 surfaces over p-adic local fields,
generalising some work of Collino. The existence of these cycles is
predicted by the poles of the local L-factor at p of the L-function of
the Abelian surface. The techniques involve using some recent work of
Bogomolov-Hassett and Tschinkel on the deformations of rational curves on
K3 surfaces.