Chow motives of genus one fibrations

Daiki Kawabe

Published 2022-01-17, updated 2022-01-27Version 2

In this paper, we prove the existence of an isomorphism of Chow motives between a genus one fibration and the associated Jacobian fibration. Using this result, we prove the Kimura finiteness of surfaces not of general type defined over an arbitrary algebraically closed field with geometric genus zero.