The derived functors of unramified cohomology

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.

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