Representability of Chow Groups of 0-Cycles and the Gysin Kernel

Abstract

The study of algebraic cycles is a highly developed and fascinating subject, which not only occupies a prominent place in Algebraic Geometry, but also shares common ground with, for example, Complex Geometry (e.g., via Hodge Conjecture), Arithmetic Geometry (e.g., via the study of rational points), Number Theory (e.g., via Tate Conjecture), Algebraic K-Theory (e.g., via Motivic Cohomology), and Mathematical Physics. In this work I will discuss the problem of the representability of Chow groups of algebraic 0-cycles on surfaces through study of the Gysin kernel which allows us to obtain useful results for studying Bloch’s conjecture and constant cycles curves (ccc).