4 papers
Simplicial presheaves of Green complexes and twisting cochains
Timothy Hosgood, Mahmoud Zeinalian
We construct three simplicial presheaves on the site of ringed spaces, and in particular on that of complex manifolds. The descent objects for these simplicial presheaves yield Tol…
Various notions of (co)simplicial (pre)sheaves
Timothy Hosgood
The phrase "(co)simplicial (pre)sheaf" can be reasonably interpreted in multiple ways. In this survey we study how the various notions familiar to the author relate to one another.…
Simplicial Chern-Weil theory for coherent analytic sheaves, part II
Timothy Hosgood
In the previous part of this diptych, we defined the notion of an admissible simplicial connection, as well as explaining how H.I. Green constructed a resolution of coherent analyt…
Simplicial Chern-Weil theory for coherent analytic sheaves, part I
Timothy Hosgood
In "Chern classes for coherent sheaves", H.I. Green constructs Chern classes in de Rham cohomology of coherent analytic sheaves. We construct here a formal -categorical…