7 papers
Parabolic geometric Eisenstein series and constant term functors
Joakim Faergeman, Andreas Hayash
We prove a compatibility between parabolic restriction of Whittaker sheaves and restriction of representations under the geometric Casselman-Shalika equivalence. To do this, we est…
Singular support for G-categories
Gurbir Dhillon, Joakim Færgeman
For a reductive group , we introduce a notion of singular support for cocomplete dualizable DG-categories equipped with a strong -action. This is done by considering the sing…
Proof of the geometric Langlands conjecture IV: ambidexterity
D. Arinkin, D. Beraldo, L. Chen +5
This paper performs the following steps toward the proof of GLC in the de Rham setting: (i) We deduce GLC for G=GL_n; (ii) We prove that the Langlands functor L_G constructed in [G…
Proof of the geometric Langlands conjecture III: compatibility with parabolic induction
Justin Campbell, Lin Chen, Joakim Faergeman +4
We establish the compatibility of the Langlands functor with the operations of Eisenstein series constant term, and deduce that the Langlands functor induces an equivalence on Eise…
Proof of the geometric Langlands conjecture II: Kac-Moody localization and the FLE
D. Arinkin, D. Beraldo, J. Campbell +6
This paper is the second in a series of five that together prove the geometric Langlands conjecture. Our goals are two-fold: (1) Formulate and prove the Fundamental Local Equivalen…
Motivic realization of rigid G-local systems on curves and tamely ramified geometric Langlands
Joakim Færgeman
For a reductive group , we prove that complex irreducible rigid -local systems with quasi-unipotent monodromies and finite order abelianization on a smooth curve are motivic,…