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On the motives of moduli of chains and Higgs bundles
We take another approach to Hitchin's strategy of computing the cohomology of moduli spaces of Higgs bundles by localization with respect to the circle-action. Our computation is done in theExpand
Kloosterman sheaves for reductive groups
Deligne constructed a remarkable local system on P 1 f 0;1g attached to a family of Kloosterman sums. Katz calculated its monodromy and asked whether there are Kloosterman sheaves for generalExpand
Existence of moduli spaces for algebraic stacks.
We provide necessary and sufficient conditions for when an algebraic stack admits a good moduli space. This theorem provides a generalization of the Keel--Mori theorem to moduli problems whoseExpand
UNIFORMIZATION OF G-BUNDLES
We show some of the conjectures of Pappas and Rapoport concerning the moduli stack BunG of G-torsors on a curve C, where G is a semisimple Bruhat-Tits group scheme on C. In particular we prove theExpand
The cohomology rings of moduli stacks of principal bundles over curves
We prove that the cohomology of the moduli stack of G-bundles on a smooth projective curve is freely generated by the Atiyah-Bott classes in arbitrary characteristic. The main techni- cal tool neededExpand
A CONJECTURE OF HAUSEL ON THE MODULI SPACE OF HIGGS BUNDLES ON A CURVE
In this survey, we review some conjectures on the cohomology of the moduli space of Higgs bundles on a curve and explain joint work with O. Garcia-Prada and A. Schmitt [9], [10] resulting in aExpand
The y-genus of the moduli space of PGL_n-Higgs bundles on a curve (for degree coprime to n)
Building on our previous joint work with A. Schmitt [7] we explain a recursive algorithm to determine the cohomology of moduli spaces of Higgs bundles on any given curve (in the coprime situation).Expand
Irreducibility of moduli of semi-stable chains and applications to U(P, q)-Higgs bundles
We give necessary and sufficient conditions for moduli spaces of semistable chains on a curve to be irreducible and non-empty. This gives information on the irreducible components of the nilpotentExpand
Cohomology of the moduli stack of coherent sheaves on a curve
We compute the cohomology of the moduli stack of coherent sheaves on a curve and find that it is a free graded algebra on infinitely many generators.
Twisted Chern classes and Gm-gerbes
Using the language of stacks one can give a simple definition of functorial Chern classes for twisted sheaves. Calculating the cohomology ring of a Gm-gerbe we observe that the twisted Chern classesExpand
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