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

Abstract

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.

revised

References in corpus (2)

• Tate Objects in Exact Categories (with appendix by Jan \vS\vtov\'ı\vcek and Jan Trlifaj)
• Adele residue symbol and Tate's central extension for multiloop Lie algebras

Cited by in corpus (3)

• Local Beilinson-Tate Operators
• The Hitchin connection in arbitrary characteristic
• Hochschild coniveau spectral sequence and the Beilinson residue