We show that the Hilbert subspace of L2(G(F)?G(A)) generated by wave packets Eisenstein series built from discrete is whole space. Together with work Lapid [17], it achieves a proof spectral theorem R.P. Langlands ([16], [19]) based on J. Bernstein and E. [6] meromorphic continuation data. I use truncation compact sets as Arthur did for local trace formula in [2].

Let $F$ be a non-Archimedean locally compact field‎. ‎Let $sigma$ and $tau$ be finite-dimensional representations of the Weil-Deligne group of $F$‎. ‎We give strong upper and lower bounds for the Artin and Swan exponents of $sigmaotimestau$ in terms of those of $sigma$ and $tau$‎. ‎We give a different lower bound in terms of $sigmaotimeschecksigma$ and $tauotimeschecktau$‎. ‎Using the Langlands...

In this note, we study conjectures of Artin and Langlands and derive the automorphy of all solvable groups of order at most 200, three groups excepted.

Given a projective variety X and a smooth projective curve C one may consider the moduli space of maps C → X. This space admits certain compactification whose points are called quasi-maps. In the last decade it has been discovered that in the case when X is a (partial) flag variety of a semi-simple algebraic group G (or, more generally, of any symmetrizable Kac-Moody Lie algebra) these compacti...

We prove a realization of the local Langlands correspondence for two-dimensional representations Weil group conductor three in cohomology Lubin–Tate curves by purely geometric method.

Matthew Lomasa, Victoria Rickarda, Fraser Miltonb, Sharon Savageb, Andrew Weirc & Adam Zemana*a College of Medicine and Health, House, University Exeter, UKb School Psychology, Life Environmental Sciences, Washington Singer, UKc Institute Neurological Langlands Drive, Glasgow, UK