26 citations · 41 across the 7 of their papers we have counts for
9 papers · 1 filter
Homotopical Algebraic Geometry II: geometric stacks and applications
Bertrand Toen, Gabriele Vezzosi
This is the second part of a series of papers devoted to develop Homotopical Algebraic Geometry. We start by defining and studying generalizations of standard notions of linear and…
Segal topoi and stacks over Segal categories
Bertrand Toen, Gabriele Vezzosi
In math.AG/0207028 we began the study of higher sheaf theory (i.e. stacks theory) on higher categories endowed with a suitable notion of topology: precisely, we defined the notions…
From HAG to DAG: derived moduli spaces
Bertrand Toen, Gabriele Vezzosi
These are expanded notes from some talks given during the fall 2002, about ``homotopical algebraic geometry'' (HAG) with special emphasis on its applications to ``derived algebraic…
Homotopical Algebraic Geometry I: Topos theory
Bertrand Toen, Gabriele Vezzosi
This is the first of a series of papers devoted to lay the foundations of Algebraic Geometry in homotopical and higher categorical contexts (for part II, see math.AG/0404373). In t…
Existence of vector bundles and global resolutions for singular surfaces
Stefan Schroeer, Gabriele Vezzosi
We prove two results about vector bundles on singular algebraic surfaces. First, on proper surfaces there are vector bundles of rank two with arbitrarily large second Chern number…
Algebraic Geometry over model categories (a general approach to derived algebraic geometry)
Bertrand Toen, Gabriele Vezzosi
For a (semi-)model category M, we define a notion of a ''homotopy'' Grothendieck topology on M, as well as its associated model category of stacks. We use this to define a notion o…