Toric vector bundles over a discrete valuation ring and Bruhat-Tits buildings
Abstract
We give a classification of rank r torus equivariant vector bundles E on a toric scheme X over a discrete valuation ring O , in terms of graded piecewise linear maps Φ from the fan of X to the (extended) building of GL ( r ) . This is an extension of Klyachko's classification of torus equivariant vector bundles on toric varieties over a field on one hand, and Mumford's classification of equivariant line bundles on toric schemes over O on the other hand. We also give a simple criterion for equivariant splitting of E into a sum of toric line bundles in terms of its piecewise linear map. Among other things, this work lays the foundations for study of arithmetic geometry of toric vector bundles.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Algebraic structures and combinatorial models
Publication details
- Journal / source
- Advances in Mathematics
- Publisher
- Elsevier BV
- Volume
- 503
- Pages
- 111265–111265
- Publication date
- 15 September 2026
- Language
- EN