Mixed resolutions and simplicial sections Academic Article uri icon

abstract

  • 0. Introduction Let K be a field of characteristic 0. In this paper we present several technical results about the geometry of K-schemes. These results were discovered in the course of work on deformation quantization in algebraic geometry, and they play a crucial role in [Ye3]. This role will be explained at the end of the introduction. The idea behind the constructions in this paper can be traced back to old work of Bott [Bo, HY]. Let π: Z → X be a morphism of K-schemes, and let U = {U(0),...,U( m)} be an open covering of X. A simplicial section σ of π, based on the covering U, consists of a family of morphisms σi: ∆q … * This work was partially supported by the US–Israel Binational Science Founda- tion. Received Decemeber 8, 2005 … Another notion we introduce is that of mixed resolution. Here we assume the K-scheme X is smooth and separated, and each of the open sets U(i) in the covering U is affine. Given a quasi-coherent OX -module M we …

publication date

  • January 1, 2007