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On the motives of moduli of chains and Higgs bundles

- O. Garc'ia-Prada, J. Heinloth, A. Schmitt
- Mathematics
- 29 April 2011

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 the… Expand

Kloosterman sheaves for reductive groups

- J. Heinloth, N. Chau, Zhiwei Yun
- Mathematics
- 16 May 2010

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 general… Expand

Existence of moduli spaces for algebraic stacks.

- J. Alper, Daniel Halpern-Leistner, J. Heinloth
- Mathematics
- 3 December 2018

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 whose… Expand

UNIFORMIZATION OF G-BUNDLES

- J. Heinloth, J. Heinloth
- 2009

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 the… Expand

The cohomology rings of moduli stacks of principal bundles over curves

- J. Heinloth, A. Schmitt
- Medicine, Mathematics
- 2010

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 needed… Expand

A CONJECTURE OF HAUSEL ON THE MODULI SPACE OF HIGGS BUNDLES ON A CURVE

- J. Heinloth
- 2014

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 a… Expand

The y-genus of the moduli space of PGL_n-Higgs bundles on a curve (for degree coprime to n)

- O. García-Prada, J. Heinloth
- Mathematics
- 24 July 2012

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

- S. Bradlow, O. García-Prada, P. Gothen, J. Heinloth
- Mathematics
- 17 March 2017

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 nilpotent… Expand

Cohomology of the moduli stack of coherent sheaves on a curve

- J. Heinloth
- Mathematics
- 19 October 2012

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

- J. Heinloth
- Mathematics
- 15 November 2005

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 classes… Expand

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