Let $X$ be a scheme of finite type over a finite field $k$, and let ${\cal L} X$ denote its arc space; in particular, ${\cal L} X(k)=X(k[[t]])$. Using the theory of Grinberg, Kazhdan, and Drinfeld on… Expand

In this article, we construct the Hitchin fibration for groups following the scheme outlined by Frenkel-Ngo in the case of SL_{2}. This construction uses as a decisive tool the Vinberg's semigroup.… Expand

abstract:We correct the calculation of IC functions on arc spaces of reductive monoids in [Bouthier, Ng\^o, and Sakellaridis, {\it Amer. J. Math.} {\bf 138} (2016), 81--108] which did not account for… Expand

In his proof of the fundamental lemma, Ngo established the product formula for the Hitchin fibration over the anisotropic locus. One expects this formula over the larger generically regular… Expand

The goal of this work is to construct a perverse t-structure on the infinity-category of l-adic LG-equivariant sheaves on the loop Lie algebra Lg and to show that the affine Grothendieck-Springer… Expand