# Simplicial Chern-Weil theory for coherent analytic sheaves, part I

@article{Hosgood2020SimplicialCT, title={Simplicial Chern-Weil theory for coherent analytic sheaves, part I}, author={Timothy Hosgood}, journal={arXiv: Algebraic Geometry}, year={2020} }

In "Chern classes for coherent sheaves", H.I. Green constructs Chern classes in de Rham cohomology of coherent analytic sheaves, but in a way that is directly amenable to being abstractified to give us a theory of simplicial connections, as well as a simplicial version of Chern-Weil theory. We construct here a formal $(\infty,1)$-categorical framework into which we can place Green's work, as well as a more general idea as to what exactly a simplicial connection should be. The result will be the… CONTINUE READING

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