Explicit Rational Equivalences of Points on Surfaces

Abstract: The Chow group of zero-cycles on a smooth projective surface X is obtained by taking the free abelian group generated by closed points on X, and declaring two elements (“zero-cycles”) to be equal if their difference is a sum of divisors of rational functions on curves in X; in this setting we say the zero-cycles are “rationally equivalent.” These Chow groups are notoriously difficult to compute; while a set of conjectures due to Bloch and Beilinson predict certain relations must hold in these groups when X is defined over a number field, there are very few non-trivial cases in which these relations have been proven to hold. In this talk, I will discuss several techniques that can be used to compute rational equivalences exhibiting some of the expected relations, in the case that X is a product of two elliptic curves over Q.

number theory

Audience: researchers in the topic

CRM-CICMA Québec Vermont Seminar Series

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