# Derived equivalent threefolds, algebraic representatives, and the coniveau filtration

## TL;DR

This paper investigates the relationship between derived equivalences of threefolds and their Chow motives, coniveau filtration, and associated abelian varieties, providing new results that support Orlov's conjecture.

## Contribution

It establishes unconditional results for threefolds over perfect fields related to the coniveau filtration and abelian varieties, advancing understanding of derived equivalences.

## Key findings

- Results on the geometric coniveau filtration for threefolds
- Connections between derived equivalences and abelian varieties
- Support for Orlov's conjecture in the context of threefolds

## Abstract

A conjecture of Orlov predicts that derived equivalent smooth projective varieties over a field have isomorphic Chow motives. The conjecture is known for curves, and was recently observed for surfaces by Huybrechts. In this paper we focus on threefolds over perfect fields, and unconditionally secure results, which are implied by Orlov's conjecture, concerning the geometric coniveau filtration, and abelian varieties attached to smooth projective varieties.