Displaying similar documents to “Central extensions of reductive groups by K 2 ”

Vectorial extensions of Jacobians

Robert F. Coleman (1990)

Annales de l'institut Fourier

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The universal vectorial extension of a curve is described in terms of the geometry of the curve.

Local-to-global extensions of representations of fundamental groups

Nicholas M. Katz (1986)

Annales de l'institut Fourier

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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...

Invariants of a quadratic form attached to a tame covering of schemes

Philippe Cassou-Noguès, Boas Erez, Martin J. Taylor (2000)

Journal de théorie des nombres de Bordeaux

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We build on preceeding work of Serre, Esnault-Kahn-Viehweg and Kahn to establish a relation between invariants, in modulo 2 étale cohomology, attached to a tamely ramified covering of schemes with odd ramification indices. The first type of invariant is constructed using a natural quadratic form obtained from the covering. In the case of an extension of Dedekind domains, mains, this form is the square root of the inverse different equipped with the trace form. In the case of a covering...