Higher Structures in Number Theory, July 3-4 2014, Nottingham

Abstracts of some talks

Fedor Bogomolov (Univ. of Nottingham/Courant Institute)

Projective geometry and non-archimedean valuations

Producing valuations from group theoretical data is a central aspect of nonabelian geometry. This talk will present a simple method to achieve that using projective geometry and a theorem on three points.

Ted Chinburg (Univ. of Pennsylvania)

Riemann-Roch theorems and adeles on surfaces

In this talk I will start by reviewing Euler characteristics for coherent sheaves and some classical Riemann-Roch formulas for them.  I will then discuss Euler characteristics for sheaves on which a finite group acts.  By the end of the talk I will describe an adelic Riemann-Roch formula on surfaces for sheaves having an action by a finite possibly non-commutative group. I will try to emphasize examples as well as open problems connected with such formulas.

Amnon Yekutieli (Ben Gurion Univ) 

High Dimensional Topological Local Fields and Residues

An n-dimensional topological local field (TLF) is a field K, endowed with a rank n valuation, and a compatible topology. TLFs arise as Beilinson completions of function fields of n-dimensional algebraic varieties along chains of points. The main feature discussed in the talk is the residue functional, which is a high dimensional generalization of the usual residue functional from the theory of complex analytic curves. 

If time permits I will also talk about some applications of the residue functional, and on the Beilinson-Tate approach to residues. 

Notes are available at this page