We prove the (generalized) coherence conjecture of Pappas and Rapoport proposed in [PR3]. As a corollary, one of the main theorems in [PR4], which describes the geometry of the special fibers of the local models for ramified unitary groups, holds unconditionally. Our proof is based on the study of the geometry (in particular certain line bundles and l-adic sheaves) of the global Schubert variet...

Apéry’s proof [13] of the irrationality of ζ(3) is now over 25 years old, and it is perhaps surprising that his methods have not yielded any significant new results (although further progress has been made on the irrationality of zeta values [1, 14]). Shortly after the initial proof, Beukers produced two elegant reinterpretations of Apéry’s arguments; the first using iterated integrals and Lege...

Apéry’s proof [11] of the irrationality of ζ(3) is now over 25 years old, and it is perhaps surprising that his methods have not yielded any significantly new results (although further progress has been made on the irrationality of zeta values [1], [12]). Shortly after the initial proof, Beukers produced two elegant reinterpretations of Apéry’s arguments; the first using iterated integrals and ...

Herrlich showed that a Mumford curve of genus g > 1 over the p-adic complex field Cp has at most 48(g− 1), 24(g− 1), 30(g− 1) or 12(g− 1) automorphisms as p = 2, 3, 5 or p > 5. The Mumford curves attaining these bounds are uniformised by normal subgroups of finite index in certain p-adic triangle groups ∆p for p ≤ 5, or in a p-adic quadrangle group p for p > 5. The finite groups attaining these...