TL;DR
This paper investigates the cohomology rings of the stack of cameral covers and related structures for complex reductive groups, providing explicit computations and extending understanding of their geometric properties.
Contribution
It computes the rational cohomology ring of the stack of cameral covers and the stack of abstract regular G-Higgs bundles, offering new algebraic insights.
Findings
Rational cohomology ring of the stack of cameral covers is explicitly computed.
Cohomology ring of the stack of spectral covers for G=GL(n) is determined.
Results extend to the stack of abstract regular G-Higgs bundles.
Abstract
We study the stack M of cameral covers for a complex reductive group G, introduced by Donagi and Gaitsgory. We compute its rational cohomology ring. In the special case G=GL(n), M is the stack of spectral covers. We also compute the cohomology ring of the stack of abstract regular G-Higgs bundles.
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