64 citations · 473 across the 56 of their papers we have counts for
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Secondary Kodaira-Spencer classes and nonabelian Dolbeault cohomology
Carlos Simpson
If is a smooth projective variety moving in a family, we define a secondary Kodaira-Spencer class for nonabelian Dolbeault cohomology of with coefficients…
Limits in -categories
Carlos Simpson
We define notions of direct and inverse limits in an -category. We prove that the -category of fibrant -categories admits direct and inverse limits. At the end w…
Mixed twistor structures
Carlos Simpson
The purpose of this paper is to introduce the notion of mixed twistor structure, a generalization of the notion of mixed Hodge structure. The utility of this notion is to make poss…
A closed model structure for -categories, internal , -stacks and generalized Seifert-Van Kampen
Carlos Simpson
We define a closed model category containing the -nerves defined by Tamsamani, and admitting internal . This allows us to construct the -category by taking the…
Algebraic (geometric) -stacks
Carlos Simpson
We propose a generalization of Artin's definition of algebraic stack, which we call {\em geometric -stack}. The main observation is that there is an inductive structure to the d…
A relative notion of algebraic Lie group and applications to -stacks
Carlos Simpson
If is a scheme of finite type over $k=\cc $, let $\Xx /S$ denote the big etale site of schemes over . We introduce {\em presentable group sheaves}, a full subcategory of the…