Alladi Ramakrishnan Hall

Business of height pairing

Souvik Goswami

University of Alberta

In algebraic geometry there is the notion of a height pairing of algebraic
cycles, which lies at the confluence of arithmetic, Hodge theory and topol-
ogy. After explaining the basic notions, we introduce new directions in this
subject. Specifically, we address an extension of Beilinson’s height pairing
to the (still conjectural) graded pieces of a Bloch-Beilinson filtration. Along
the way, we use machineries from arithmetic intersection theory to provide
an example computation.