A DG guide to Voevodsky's motives
We give a concise exposition of Voevodsky's theory of motives.
math.AG↗
arXiv subjects
V. Vologodsky
Publications and source records attributed to V. Vologodsky.
Gamma-functions of representations and lifting
Let G be the group of points of a quasi-split reductive algebraic group over a local field F. It follows from the local Langlands conjectures that to every non-trivial additive character of F and every representation of the Langlands dual group of F one can associate certain meromorphic function on the set of isomorphism classed of irreducible representations of G (which we call gamma-functions). In this paper we describe a general framework for an explicit construction of these gamma-functions. We make this idea precise in certain special cases. As a byproduct we give explicit conjectural formulas for the representation $l_E(θ)$ of the group GL(n,F) associated to a character $θ$ of the multiplicative group $E^*$ of a separable extension E of F of degree n. We also describe a conjectural analogue of the Poisson summation formula associated to a representation of the Langlands dual group, which implies the existence of the meromorphic continuation and functional equation for the corresponding automorphic L-functions.
math.AG↗