Differential operators on projective modules

Details Differential operators on projective modules Differential operators on projective modules

2011-10-22

arxiv.org/abs/1110.4966v6

Mathematics

Algebraic Geometry

Scientific paper

In this paper we give explicit formulas for differential operators on a finitely generated projective module E on an arbitrary commutative unital ring A. We use the differential operators constructed to give a simple formula for the curvature of a connection on a Lie-Rinehart algebra in terms of the fundamental matrix of E. As a consequence we prove the first Chern class of E with values in Lie-Rinehart cohomology of L is zero. As a corollary we prove the first Chern class of a finitely generated projective module E on a regular K-algebra A of finite type over a field K with values in DeRham cohomology is zero. We also consider the notion of a stratification on the module E induced by a projective basis. It turns out few stratifications are induced by a projective basis.

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