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One of the conjectural properties of a Langlands correspondence is its compatibility with endoscopic induction. DeBacker and Reeder have recently constructed a partial local Langlands correspondence for p-adic groups, focusing on L-packets consisting of depth-zero supercuspidal representations. In this paper we prove the conjectural endoscopic transfer for these L-packets.
Any quasi-isometry of the curve complex is bounded distance from a simplicial automorphism. As a consequence, the quasi-isometry type of the curve complex determines the homeomorphism type of the surface.
We construct the -adic zeta function for a one-dimensional (as a -adic Lie extension) noncommutative -extension of a totally real number field such that the finite part of its Galois group is a -group of exponent . We first calculate the Whitehead groups of the Iwasawa algebra and its canonical Ore localization by using Oliver and Taylor's theory of integral logarithms. This calculation reduces the existence of the noncommutative -adic zeta function to certain congruences between abelian -adic zeta pseudomeasures. Then we finally verify these congruences by using Deligne and Ribet's theory and a certain inductive technique. As an application we prove a special case of (the -part of) the noncommutative equivariant Tamagawa number conjecture for critical Tate motives.