Online Archive of University of Virginia Scholarship
Zero Cycles on Products of Elliptic Curves with Supersingular Reduction47 views
Author
De Las Penas Castano, Alejandro, Mathematics - Graduate School of Arts and Sciences, University of Virginia
Advisors
Gazaki, Evangelia, AS-Mathematics (MATH), University of Virginia
Abstract
For a product of two elliptic curves over a p-adic field with good supersingular reduction, we produce infinitely many rational equivalences in the Chow group of zero cycles via genus 2 covers of both elliptic curves. We use this to obtain evidence for a conjecture of Colliot-Thélène about the structure of the Albanese kernel. Furthermore, we describe an algorithm that can produce these rational equivalences, and in some cases prove the p-divisibility of the generators of the Albanese kernel coming from the rational points of the elliptic curves.
Degree
PHD (Doctor of Philosophy)
Keywords
elliptic curves; local fields; supersingular; Chow; zero cycles; Albanese
De Las Penas Castano, Alejandro. Zero Cycles on Products of Elliptic Curves with Supersingular Reduction. University of Virginia, Mathematics - Graduate School of Arts and Sciences, PHD (Doctor of Philosophy), 2026-04-29, https://doi.org/10.18130/q8dh-1e36.
