On jets, extensions and characteristic classes II
Abstract
In this paper we define and study generalized Atiyah classes for quasi coherent sheaves relative to arbitrary morphisms of schemes. We use derivations and quasi coherent sheaves of left and right O-modules to define a generalized first order jet bundle J(E) and a generalized Atiyah sequence for E. The generalized jet bundle J(E) is a left and right module over a sheaf J of associative rings on X. The sheaf J is an extension of O with a sheaf I of two sided ideals of square zero. The Atiyah sequence gives rise to a generalized Atiyah class c(E) with the property that c(E)=0 if and only if the left structure on J(E) is O-isomorphic to the right structure on J(E). We give examples where c(E)=0 and c(E)\neq 0 hence the class c(E) is a non trivial characteristic class.
Keywords
Cite
@article{arxiv.1006.0593,
title = {On jets, extensions and characteristic classes II},
author = {Helge Øystein Maakestad},
journal= {arXiv preprint arXiv:1006.0593},
year = {2020}
}
Comments
This paper is a revised and extended version of a section in the paper "On jets, extensions and characteristic classes". A section with explicit examples is added. Some proofs are shortened