Vector Bundles and Arithmetical Groups I. The higher Bruhat-Tits tree
Abstract
Description
We define and study a simplicial complex which is a homogeneous space for the group $PGL(2, K)$ over a two-dimensional local field $K$. The complex is a generalization of the tree studied by F. Bruhat, J. Tits, J.-P. Serre and P. Cartier in the 60's and early 70's. Such complex can be canonically attached to the triples $x \in C \subset X$ where $X$ is an algebraic surface, $C$ is an irreducible curve and $x$ is a smooth point on $C$ and $X$. This construction can be used for a description of the isomorphism set of vector bundles on $X$.
to appear in an english translation of the Proc. Steklov Math. Institute, vol. 208 33 pages, LaTeX, emlines.sty
to appear in an english translation of the Proc. Steklov Math. Institute, vol. 208 33 pages, LaTeX, emlines.sty