26 citations · 42 across the 7 of their papers we have counts for
14 papers
Derived Hall Algebras
B. Toen
The purpose of this work is to define a derived Hall algebra , associated to any dg-category (under some finiteness conditions). Our main theorem states that $…
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…
"Brave New" Algebraic Geometry and global derived moduli spaces of ring spectra
Bertrand Toen, Gabriele Vezzosi
We develop homotopical algebraic geometry (see math.AG/0207028) in the special context where the base symmetric monoidal model category is the category S of spectra, i.e. what migh…
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…
A remark on K-theory and S-categories
Bertrand Toen, Gabriele Vezzosi
It is now well known that the K-theory of a Waldhausen category depends on more than just its (triangulated) homotopy category (see [Schlichting]). The purpose of this note is to s…