%0 Generic %1 loeser2019motivic %A Loeser, François %A Wyss, Dimitri %D 2019 %K hitchin %T Motivic Integration on the Hitchin Fibration %U http://arxiv.org/abs/1912.11638 %X We prove that the moduli spaces of twisted $SL_n$ and $PGL_n$-Higgs bundles on a smooth projective curve have the same (stringy) class in the Grothendieck ring of rational Chow motives. On the level of Hodge numbers this was conjectured by Hausel and Thaddeus, and recently proven by Groechenig, Ziegler and the second author. To adapt their argument, which relies on p-adic integration, we use a version of motivic integration with values in rational Chow motives and the geometry of Néron models to evaluate such integrals on Hitchin fibers.

@misc{loeser2019motivic, abstract = {We prove that the moduli spaces of twisted $\mathrm{SL}_n$ and $\mathrm{PGL}_n$-Higgs bundles on a smooth projective curve have the same (stringy) class in the Grothendieck ring of rational Chow motives. On the level of Hodge numbers this was conjectured by Hausel and Thaddeus, and recently proven by Groechenig, Ziegler and the second author. To adapt their argument, which relies on p-adic integration, we use a version of motivic integration with values in rational Chow motives and the geometry of N\'eron models to evaluate such integrals on Hitchin fibers.}, added-at = {2019-12-31T12:00:06.000+0100}, author = {Loeser, François and Wyss, Dimitri}, biburl = {https://www.bibsonomy.org/bibtex/234baaf8f1d296ba80678298f9d96f92f/simonechiarello}, description = {Motivic Integration on the Hitchin Fibration}, interhash = {add20f9372cd73e0d207730e8dca3def}, intrahash = {34baaf8f1d296ba80678298f9d96f92f}, keywords = {hitchin}, note = {cite arxiv:1912.11638Comment: 34 pages, comments welcome}, timestamp = {2019-12-31T12:00:06.000+0100}, title = {Motivic Integration on the Hitchin Fibration}, url = {http://arxiv.org/abs/1912.11638}, year = 2019 }