Motivic equivalence under semismall flops

TL;DR

This paper demonstrates that semismall smooth flops preserve the Chow motives of smooth projective varieties, establishing a motive isomorphism via intersection complex pushforwards.

Contribution

It introduces a method to compare Chow motives under semismall flops using intersection complexes, extending motive invariance results.

Findings

Chow motives are preserved under semismall smooth flops.

Isomorphism of motives is established non-canonically.

Applicable over any noetherian local ring coefficients.

Abstract

We prove that under semismall smooth flops, smooth projective varieties have (non-canonically) isomorphic Chow motives with coefficients in any noetherian local ring $\Lambda$ by comparing the pushforward of the constant intersection complexes through flopping contractions.