Adjoint Swan Conductors I: The Essentially Tame Case

The Laplace operator is essentially self-adjoint

Some Endoscopic Properties of The Essentially Tame Jacquet-Langlands Correspondence

Let F be a non-Archimedean local field of characteristic 0 and G be an inner form of the general linear group G = GLn over F . We show that the rectifying character appearing in the essentially tame Jacquet-Langlands correspondence of Bushnell and Henniart for G and G can be factorized into a product of some special characters, called zeta-data in this paper, in the theory of endoscopy of Langl...

Swan conductors on the boundary of Lubin-Tate spaces

Lubin-Tate spaces of dimension one are finite étale covers of the nonarchimedian open unit disk. We compute certain invariants which measure the ramification of this cover over the boundary of the disk.

Swan Conductors and Torsion in the Logarithmic de Rham Complex

We prove, for an arithmetic scheme X/S over a discrete valuation ring whose special fiber is a strict normal crossings divisor in X, that the Swan conductor of X/S is equal to the Euler characteristic of the torsion in the logarithmic de Rham complex of X/S. This is a precise logarithmic analog of a theorem by Bloch [1].

2 00 6 Swan conductors for p - adic differential modules , I : A local construction

We define a numerical invariant, the differential Swan conductor, for certain differential modules on a rigid analytic annulus over a p-adic field. This gives a definition of a conductor for p-adic Galois representations with finite local monodromy over an equal characteristic discretely valued field, which agrees with the usual Swan conductor when the residue field is perfect. We also establis...