Analytic Tate spaces and reciprocity laws (Q2927904)

The author introduces an analytic version of the notion of Tate spaces. An \textit{analytic Tate space} is defined as a topological vector space splitting as the direct sum of a nuclear Fréchet space and the strong dual of a nuclear Fréchet space. The ring of Laurent power series \(k((t))\) is an example of a Tate space which is also an analytic Tate space. Others examples are given, including \(\mathcal{O}_{\hat{0}}\), the ring of germs of analytic functions on a punctured neighborhood of \(0\in \mathbb{C}\).NEWLINENEWLINEThe aim of the paper is to show that some results valid for Tate spaces do extend to the new analytic situation. The author defines commutator symbols, and proves reciprocity laws for algebraic curves, in the complex and \(p\)-adic analytic cases.