  We consider a functional analytic variant of the notion of Tate space, namely
the category of those topological vector spaces which have a direct sum
decomposition where one summand is nuclear Frechet space and the other is the
dual of a nuclear Frechet. We show that, both in the complex and in the p-adic
setting, one can use this formalism to define symbols for analytic functions
which satisfy Weil-type reciprocity laws.

Algebraic Geometry;Functional Analysis;Number Theory