Dans cet article, nous proposons une démonstration pour des conjectures de Langlands,
Shelstad et Waldspurger plus connues sous le nom de lemme fondamental pour les …

For any reductive group $ G $ over a global function field, we use the cohomology of $ G $-
shtukas with multiple modifications and the geometric Satake equivalence to prove the …

We provide necessary and sufficient conditions for when an algebraic stack admits a good
moduli space and prove a semistable reduction theorem for points of algebraic stacks …

For G= GL 2, PGL 2, SL 2 we prove that the perverse filtration associated with the Hitchin
map on the rational cohomology of the moduli space of twisted G-Higgs bundles on a …

Motivated by a 1993 conjecture of Stanley and Stembridge, Shareshian and Wachs
conjectured that the characteristic map takes the character of the dot action of the symmetric …

We conjecturally extract the triply graded Khovanov–Rozansky homology of the (m, n) torus
knot from the unique finite-dimensional simple representation of the rational DAHA of type A …

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

We prove that the number of geometrically indecomposable vector bundles of fixed rank r
and degree d over a smooth projective curve X defined over a finite field is given by a …

We provide geometric constructions of modules over the graded Cherednik algebra H ν gr
and the rational Cherednik algebra H ν rat attached to a simple algebraic group G together …

Abstract We define the Heegner--Drinfeld cycle on the moduli stack of Drinfeld Shtukas of
rank two with r-modifications for an even integer r. We prove an identity between (1) the r-th …