Toric schemes over a DVR, vector bundles and affine buildings

Thursday, September 23, 2021 - 11:00

Zoom Meeting ID: 973 0230 7263

Speaker Information
Kiumars Kaveh

Abstract or Additional Information

This is a report on a work in progress with Chris Manon and Boris Tsvelikhovsky. Motivated by problems in arithmetic geometry, it is natural to consider algebraic varieties defined over a DVR (discrete valuation ring). After recalling some basic concepts about toric varieties, we review the classification of toric schemes defined over a DVR (going back to Mumford in 70’s). We will then review some basic definitions from theory of buildings and in particular recall Tits and Bruhat-Tits buildings of SL(n) and GL(n). We will then discuss our new results on classification of equivariant vector bundles on toric schemes in terms of “piecewise affine maps” to the Bruhat-Tits building of GL(n).