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Local-to-global extensions of representations of fundamental groups

Nicholas M. Katz (1986)

Annales de l'institut Fourier

Let K be a field of characteristic p > 0 , C a proper, smooth, geometrically connected curve over K , and 0 and ∞ two K -rational points on C . We show that any representation of the local Galois group at ∞ extends to a representation of the fundamental group of C - { 0 , ∞ } which is tamely ramified at 0, provided either that K is separately closed or that C is P 1 . 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...

Lubin-Tate formal groups and module structure over Hopf orders

Werner Bley, Robert Boltje (1999)

Journal de théorie des nombres de Bordeaux

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...

Modified proof of a local analogue of the Grothendieck conjecture

Victor Abrashkin (2010)

Journal de Théorie des Nombres de Bordeaux

A local analogue of the Grothendieck Conjecture is an equivalence between the category of complete discrete valuation fields K with finite residue fields of characteristic p ≠ 0 and the category of absolute Galois groups of fields K together with their ramification filtrations. The case of characteristic 0 fields K was studied by Mochizuki several years ago. Then the author of this paper proved it by a different method in the case p > 2 (but with no restrictions on the characteristic of K ). In this paper...

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