Yakov Varshavsky

The Tannakian formalism and the Langlands conjectures

Let H be a connected reductive group over an algebraically closed field of characteristic zero, and let G be an abstract group. In this note we show that every homomorphism from the Grothendieck semiring of H to that of G which maps irreducible representations to irreducibles, comes from a group homomorphism from G to H. We also connect this result with the Langlands conjectures.

Endoscopic decomposition of certain depth zero representations

We construct an endoscopic decomposition for local L-packets associated to irreducible cuspidal Deligne-Lusztig representations. Moreover, the obtained decomposition is compatible with inner twistings.

On the depth r Bernstein projector

In this paper we prove an explicit formula for the Bernstein projector to representations of depth

A proof of a generalization of Deligne’s conjecture

\le r

Geometric approach to parabolic induction

≤r. As a consequence, we show that the depth zero Bernstein projector is supported on topologically unipotent elements and it is equal to the restriction of the character of the Steinberg representation. As another application, we deduce that the depth r Bernstein projector is stable. Moreover, for integral depths our proof is purely local.

Lefschetz–Verdier Trace Formula and a Generalization of a Theorem of Fujiwara

We construct an endoscopic decomposition for local L-packets associated to irreducible cuspidal Deligne-Lusztig representations. Moreover, the obtained decomposition is compatible with inner twistings.

Moduli spaces of principal F -bundles

The goal of this paper is to give a simple proof of Delignes conjecture (proven by Fujiwara) and to generalize it to the situation appearing in our joint project with David Kazhdan on the global Langlands correspondence over function fields. Our proof holds in the realm of ordinary algebraic geometry and does not use rigid geometry.

ON ENDOSCOPIC TRANSFER OF DELIGNE-LUSZTIG FUNCTIONS

In this note we formulate and give a self-contained proof of the Yoneda lemma for ∞-categories in the language of complete Segal spaces.