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Let be a rational prime and a complete discrete valuation field with residue field of positive characteristic . When is finite, generalizing the theory of Deligne [1], we construct in [10] and [11] a theory of local -constants for representations, over a complete local ring with an algebraically closed residue field of characteristic , of the Weil group of . In this paper, we generalize the results in [10] and [11] to the case where is an arbitrary perfect field.
The -adic local Langlands correspondence for attaches to any -dimensional irreducible -adic representation of an admissible unitary representation of . The unitary principal series of are those corresponding to trianguline representations. In this article, for , using the machinery of Colmez, we determine the space of locally analytic vectors for all non-exceptional unitary principal series of by proving a conjecture of Emerton.
Let be a field of characteristic , a proper, smooth, geometrically connected curve over , and 0 and two -rational points on . We show that any representation of the local Galois group at extends to a representation of the fundamental group of which is tamely ramified at 0, provided either that is separately closed or that is . In the latter case, we show there exists a unique such extension, called “canonical”, with the property that the image of the geometric fundamental group...
Over the last years Hopf orders have played an important role in the study of integral module structures arising in arithmetic geometry in various situations. We axiomatize these situations and discuss the properties of the (integral) Hopf algebra structures which are of interest in this general setting. In particular, we emphasize the role of resolvents for explicit computations. As an illustration we apply our results to determine the Hopf module structure of the ring of integers in relative Lubin-Tate...
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