Vector Bundles and Arithmetical Groups I. The higher Bruhat-Tits tree

1996/05/07 by A. N. Parshin, Parshin, A. N.
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Quantum Algebra (math.QA) #alg-geom #math.AG #math.QA #q-alg

paper · pdf · doi:10.48550/arxiv.alg-geom/9605001

to appear in an english translation of the Proc. Steklov Math. Institute, vol. 208 33 pages, LaTeX, emlines.sty

arxiv created 1996/05/07 · arxiv updated 2009/11/30

Abstract

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 ∈ C ⊂ 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.

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