London Algebra Colloquium abstract

Multiplicity in difference geometry

Konstantin Ardakov (Queen Mary), 6th December 2012


Classical commutative rigid analytic spaces were introduced by John Tate in the 1960s with number-theoretic applications in mind. They are defined in terms of a particular p-adic completion of the polynomial algebra, called the Tate algebra. When we replace the polynomial algebra by the Weyl algebra and perform the same construction, we obtain the so-called Tate–Weyl algebra. Using these rings, we build a sheaf D^ of non-commutative rings on any smooth rigid analytic space X that can be viewed as a quantisation of the cotangent bundle of X. If time permits, I’ll explain the connection between D^-modules and the p-adic representation theory of compact p-adic Lie groups.

This is joint work with Simon Wadsley.