Whereas usual Hodge theory concerns mainly the usual or abelian cohomology of an algebraic variety—or eventually the rational homotopy theory or nilpotent completion of π1 which are in some sense… (More)

Let X be a compact connected Kähler manifold, x ∈ X and Γ = π1(X,x). Let ρ : Γ → GLN (C) be a finite dimensional semisimple representation. We assume ρ to be the monodromy of a given polarized C-VHS… (More)

The purpose of this paper is to develop some additional techniques for the weak ncategories defined by Tamsamani in [27] (which he calls n-nerves). The goal is to be able to define the internal… (More)

The purpose of this paper is to introduce the notion of mixed twistor structure as a generalization of the notion of mixed Hodge structure. Recall that a mixed Hodge structure is a vector space V… (More)

It has been difficult to see precisely the role played by strict n-categories in the nascent theory of n-categories, particularly as related to n-truncated homotopy types of spaces. We propose to… (More)

In [2] Baez and Dolan established their stabilization hypothesis as one of a list of the key properties that a good theory of higher categories should have. It is the analogue for n-categories of the… (More)

In SGA 4 [1], one of the principal building blocks of the theory of topoi is Giraud’s theorem, which says that the condition of a 1-category A being the category of sheaves on a site, may be… (More)

We construct a locally geometric ∞-stack MHod(X,Perf) of perfect complexes with λ-connection structure on a smooth projective variety X. This maps to A1/Gm, so it can be considered as the Hodge… (More)