#### Vol. 300, No. 2, 2019

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Hochschild coniveau spectral sequence and the Beilinson residue

### Oliver Braunling and Jesse Wolfson

Vol. 300 (2019), No. 2, 257–329
##### Abstract

Higher-dimensional residues can be constructed either following Grothendieck–Hartshorne using local cohomology, or following Tate–Beilinson using Lie algebra homology. We show that there is a natural link: we develop the Hochschild analogue of the coniveau spectral sequence. The rows of our spectral sequence look a lot like the Cousin complexes in Hartshorne’s Residues and duality, which live in the framework of coherent cohomology. We prove that the complexes agree by an “HKR isomorphism with supports”. Using the close ties of Hochschild homology to Lie algebra homology, this yields a direct comparison.

##### Keywords
adeles, Tate residue, Beilinson residue, Tate central extension, residue symbol, Cousin complex, Tate object
Primary: 19D55