On the local residue symbol in the style of Tate and Beilinson
  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. 
Oliver Braunling
math.AG