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Publications Influence

Geometry of cohomology support loci for local systems I

- D. Arapura
- Mathematics
- 7 December 1996

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 under… Expand

171 31- PDF

The Leray spectral sequence is motivic

- D. Arapura
- Mathematics
- 13 January 2003

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 of… Expand

60 11- PDF

Motivation for Hodge cycles

- D. Arapura
- Mathematics
- 21 January 2005

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

39 7- PDF

On the fundamental group of a compact Kähler manifold

- D. Arapura, P. Bressler, M. Ramachandran
- Mathematics
- 1 December 1992

46 5

An Abelian Category of Motivic Sheaves

- D. Arapura
- Mathematics
- 1 January 2008

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 faithful… Expand

26 4- PDF

Solvable Fundamental Groups of Algebraic Varieties and Käler Manifolds

- D. Arapura, M. Nori
- Mathematics
- 24 June 1997

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

49 4- PDF

Intermediate Jacobians and Hodge structures of moduli spaces

- D. Arapura, P. Sastry
- Mathematics
- 9 August 1999

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.

17 3- PDF

VANISHING CYCLES

- D. Arapura
- 2013

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. The… Expand

7 3- PDF

The Hodge theoretic fundamental group and its cohomology

- D. Arapura
- Mathematics
- 24 February 2009

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 and… Expand

9 2- PDF

Partial regularity and amplitude

- D. Arapura
- Mathematics
- 26 January 2004

<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 to… Expand

13 2- PDF

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