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 $p$-adic zeta function for a one-dimensional (as a $p$-adic Lie extension) noncommutative $p$-extension $F_{\infty }$ of a totally real number field $F$ such that the finite part of its Galois group $G$ is a $p$-group of exponent $p$. We first calculate the Whitehead groups of the Iwasawa algebra $\Lambda (G)$ and its canonical Ore localization $\Lambda (G{)}_S$ by using Oliver and Taylor's theory of integral logarithms. This calculation reduces the existence of the noncommutative $p$-adic zeta function to certain congruences between abelian $p$-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 $p$-part of) the noncommutative equivariant Tamagawa number conjecture for critical Tate motives.

We demonstrate the existence of a metric of positive sectional curvature on the $3$-Sasakian $7$-manifold over Hitchin's self-dual Einstein orbifold with $k=5$.