R. Kottwitz | Searcharxiv

arXiv2012

On Splitting Invariants and Sign Conventions in Endoscopic Transfer

The transfer factors for standard endoscopy involve, among other things, the Langlands-Shelstad splitting invariant. This note introduces a twisted version of that splitting invariant. The twisted splitting invariant is then used to define a better twisted factor $Δ_I$. In addition we correct a sign error in the definition of twisted transfers. There are two ways to correct the sign error. One way yields twisted transfer factors $Δ'$ that are compatible with the classical Langlands correspondence. The other way yields twisted transfer factors $Δ_D$ that are compatible with a renormalized version of the Langlands correspondence.

math.RT↗

arXiv2002

On the existence of F-crystals

Let (N,F) be an F-isocrystal, with associated Newton vector νin (Q^n)_+. To any lattice M in N (an F-crystal) is associated its Hodge vector μ(M) in (Z^n)_+. By Mazur's inequality we have μ(M)>= ν. We show that, conversely, for any μin (Z^n)_+ with μ>= ν, there exists a lattice M in N such that μ=μ(M). We also give variants of this existence theorem for symplectic F-isocrystals, and for periodic lattice chains.

math.NT↗