# Reciprocity laws for higher-dimensional varieties

## Michael Groechenig (Imperial College)

The Contou-Carrère symbol was introduced in the 90s in order to study a geometric analogue of local class field theory. Contou-Carrère proved that this symbol induces a self-duality of loop groups, which can be understood as the local analogue (in the sense of number theory) of the self-duality of Jacobian varieties of curves (a global object, in the sense of number theory). The link between the local and global side of the story is provided by Weil reciprocity. In this talk we introduce a higher-dimensional generalization of the Contou-Carrère symbol, and show that it satisfies reciprocity. Our construction is based on certain (higher) gerbes arising naturally on the automorphism groups of infinite-dimensional vector bundles, as well as their connection to algebraic K-theory of schemes. This is joint work with O. Braunling and J. Wolfson.

Tuesday, September 30th, at 4:00pm in HBH 227

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