The derived functors of unramified cohomology

Bruno Kahn (1) , R. Sujatha (2)

1 IMJ - Institut de Mathématiques de Jussieu
2 School of Mathematics [TIFR]

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.

Domaines: Géométrie algébrique [math.AG]

Bruno Kahn, R. Sujatha. The derived functors of unramified cohomology. Selecta Mathematica (New Series), 2018, 24 (2), pp.1121-1146. ⟨10.1007/s00029-017-0359-x⟩. ⟨hal-02740413⟩