On the local residue symbol in the style of Tate and Beilinson
||Residues, residue symbol, Tate residue, Grothendieck duality, adeles.|
||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.
Freiburg Institute for Advanced Studies (FRIAS), University of Freiburg, Albertstrasse 19, D-79104 Freiburg, Germany