The author proves an equality of gerbe-twisted p-adic integrals on SLn and PGLn Higgs bundle moduli spaces for arbitrary rank and degree, generalizing the coprime-case result of Groechenig, Wyss, and Ziegler.
Global topology of the Hitchin system
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abstract
Here we survey several results and conjectures on the cohomology of the total space of the Hitchin system: the moduli space of semi-stable rank n and degree d Higgs bundles on a complex algebraic curve C. The picture emerging is a dynamic mixture of ideas originating in theoretical physics such as gauge theory and mirror symmetry, Weil conjectures in arithmetic algebraic geometry, representation theory of finite groups of Lie type and Langlands duality in number theory.
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Non-archimedean topological mirror symmetry for $SL_n$ and $PGL_n$ Higgs bundles
The author proves an equality of gerbe-twisted p-adic integrals on SLn and PGLn Higgs bundle moduli spaces for arbitrary rank and degree, generalizing the coprime-case result of Groechenig, Wyss, and Ziegler.