%0 Generic %1 groechenig2017mirror %A Groechenig, Michael %A Wyss, Dimitri %A Ziegler, Paul %D 2017 %K higgs %T Mirror symmetry for moduli spaces of Higgs bundles via p-adic integration %U http://arxiv.org/abs/1707.06417 %X We prove the Topological Mirror Symmetry Conjecture by Hausel-Thaddeus for smooth moduli spaces of Higgs bundles of type $SL_n$ and $PGL_n$. More precisely, we establish an equality of stringy Hodge numbers for certain pairs of algebraic orbifolds generically fibred into dual abelian varieties. Our proof utilises p-adic integration relative to the fibres, and interprets canonical gerbes present on these moduli spaces as characters on the Hitchin fibres using Tate duality. Furthermore we prove for $d$ coprime to $n$, that the number of rank $n$ Higgs bundles of degree $d$ over a fixed curve defined over a finite field, is independent of $d$. This proves a conjecture by Mozgovoy--Schiffman in the coprime case.

@misc{groechenig2017mirror, abstract = {We prove the Topological Mirror Symmetry Conjecture by Hausel-Thaddeus for smooth moduli spaces of Higgs bundles of type $\operatorname{SL}_n$ and $\operatorname{PGL}_n$. More precisely, we establish an equality of stringy Hodge numbers for certain pairs of algebraic orbifolds generically fibred into dual abelian varieties. Our proof utilises p-adic integration relative to the fibres, and interprets canonical gerbes present on these moduli spaces as characters on the Hitchin fibres using Tate duality. Furthermore we prove for $d$ coprime to $n$, that the number of rank $n$ Higgs bundles of degree $d$ over a fixed curve defined over a finite field, is independent of $d$. This proves a conjecture by Mozgovoy--Schiffman in the coprime case.}, added-at = {2019-10-29T10:11:10.000+0100}, author = {Groechenig, Michael and Wyss, Dimitri and Ziegler, Paul}, biburl = {https://www.bibsonomy.org/bibtex/2b91e4c475ce689287407e34498ec96e1/simonechiarello}, description = {Mirror symmetry for moduli spaces of Higgs bundles via p-adic integration}, interhash = {007fcc9d76e2d18b400ba3001b248f4c}, intrahash = {b91e4c475ce689287407e34498ec96e1}, keywords = {higgs}, note = {cite arxiv:1707.06417Comment: Various part of the article have been revised}, timestamp = {2019-10-29T10:11:10.000+0100}, title = {Mirror symmetry for moduli spaces of Higgs bundles via p-adic integration}, url = {http://arxiv.org/abs/1707.06417}, year = 2017 }