394 research outputs found
The complexity of central series in nilpotent computable groups
AbstractThe terms of the upper and lower central series of a nilpotent computable group have computably enumerable Turing degree. We show that the Turing degrees of these terms are independent even when restricted to groups which admit computable orders
Degenerations and limit Frobenius structures in rigid cohomology
We introduce a "limiting Frobenius structure" attached to any degeneration of
projective varieties over a finite field of characteristic p which satisfies a
p-adic lifting assumption. Our limiting Frobenius structure is shown to be
effectively computable in an appropriate sense for a degeneration of projective
hypersurfaces. We conjecture that the limiting Frobenius structure relates to
the rigid cohomology of a semistable limit of the degeneration through an
analogue of the Clemens-Schmidt exact sequence. Our construction is
illustrated, and conjecture supported, by a selection of explicit examples.Comment: 41 page
Kontsevich's Universal Formula for Deformation Quantization and the Campbell-Baker-Hausdorff Formula, I
We relate a universal formula for the deformation quantization of arbitrary
Poisson structures proposed by Maxim Kontsevich to the Campbell-Baker-Hausdorff
formula. Our basic thesis is that exponentiating a suitable deformation of the
Poisson structure provides a prototype for such universal formulae.Comment: 48 pages, over 90 (small) epsf figures, uses some ams-latex package
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