New York Journal of Mathematics
Volume 24 (2018), 458-513


Oliver Braunling

On the local residue symbol in the style of Tate and Beilinson

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Published: August 20,2018.
Keywords: Residues, residue symbol, Tate residue, Grothendieck duality, adeles.
Subject: Primary 32A27; 14B15; Secondary 14F05; 32C37.

Tate gave a famous construction of the residue symbol on curves by using some non-commutative operator algebra in the context of algebraic geometry. We explain Beilinson's multidimensional generalization, which is not so well-documented in the literature. We provide a new approach using Hochschild homology.


This work has been partially supported by the DFG SFB/TR45 "Periods, moduli spaces, and arithmetic of algebraic varieties" and the Alexander von Humboldt Stiftung.

Author information

Oliver Braunling:
Freiburg Institute for Advanced Studies (FRIAS), University of Freiburg, Albertstrasse 19, D-79104 Freiburg, Germany