The derived functors of unramified cohomology

TL;DR

This paper investigates the derived functors of unramified cohomology for specific sheaves, revealing connections with classical invariants like Griffiths groups and indecomposable cycles in algebraic geometry.

Contribution

It introduces new insights into the derived functors of unramified cohomology and links them to classical cycle-theoretic invariants of smooth projective varieties.

Findings

Connections with Griffiths group and indecomposable (2,1)-cycles

New relationships between unramified cohomology and classical invariants

Enhanced understanding of cycle-theoretic invariants in algebraic geometry

Abstract

We study the first "derived functors of unramified cohomology" in the sense of arXiv:1506.08385 [math.AG], applied to the sheaves $\mathbf{G}_m$ and $\mathcal{K}_2$. We find interesting connections with classical cycle-theoretic invariants of smooth projective varieties, involving notably a version of the Griffiths group, and the indecomposable $(2,1)$-cycles.