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Geometry of cohomology support loci for local systems I
Let X be a Zariski open subset of a compact Kaehler manifold. In this paper, we study the set $\Sigma^k(X)$ of one dimensional local systems on X with nonvanishing kth cohomology. We show that underExpand
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The Leray spectral sequence is motivic
Our goal is to prove that the Leray spectral sequence associated to a map of algebraic varieties is motivic in the following sense: If the singular cohomology groups of the category ofExpand
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Motivation for Hodge cycles
Given two smooth projective varieties X and Y, X is defined to motivate Y if the motive of Y is contained in the tensor category generated by X. Some techniques are given for checking this condition.Expand
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An Abelian Category of Motivic Sheaves
The goal of this paper is to construct a category of motivic "sheaves" on an algebraic variety defined over a subfield of C, using Nori's method. This categoryis abelian and it possesses faithfulExpand
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Solvable Fundamental Groups of Algebraic Varieties and Käler Manifolds
It is shown that if the fundamental group of a normal algebraic variety, respectively Zariski open subset of a compact Kähler manifold, is solvable with a faithful linear representation over Q,Expand
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Intermediate Jacobians and Hodge structures of moduli spaces
The mixed Hodge structure on the low degree cohomology of the moduli space of vector bundles on a curve is studied. Analysis of the third cohomology yields a new proof of a Torelli theorem.
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VANISHING CYCLES
We will start with the classical picture. Suppose that f : X → C is a morphism from a nonsingular variety. The fiber X0 = f −1(0) may be singular, but the nearby fibers Xt, 0 < |t| < 1 are not. TheExpand
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The Hodge theoretic fundamental group and its cohomology
In this paper, we explore a notion of nonabelian Hodge structure on the fundamental group of an algebraic variety. This is approach is compared to some alternative approaches due to Morgan, Hain andExpand
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Partial regularity and amplitude
<abstract abstract-type="TeX"><p>The author continues the study of Frobenius amplitude, introduced in an earlier paper, and compares this to various other positivity notions. These are applied toExpand
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