منابع مشابه
Relative Completions
We compute the completion of the groups SLn(Zt]) and SLn (Zt;t ?1 ]) relative to the obvious homomorphisms to SLn (Q); this is a generalization of the classical Malcev completion. We also make partial computations of the rational second cohomology of these groups.
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We extend arbitrary group completions to the category of pairs (G, N) where G is a group and N is a normal subgroup of G. Relative localizations are defined as special cases. Our construction is a group-theoretical analogue of fibrewise completion and fibrewise localization in homotopy theory, and generalizes earlier work on relative localization of groups at primes. We use our approach to find...
متن کاملRelative pro-l completions of Teichmüller groups
Let Γg,n, for 2g − 2 + n > 0, be the Teichmüller group of an n-punctured genus g compact Riemann surface Sg,n and let Γ(l), for a prime l ≥ 2, be the abelian level defined by the kernel of the natural representation Γg,n → Sp2g(Z/l). The pro-l completion Γ(l)(l) of Γ(l) defines a profinite completion of Γg,n, which we call the relative pro-l completion and denote by Γ (l) g,n. There is a natura...
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We compute the completion of the special linear group over the coordinate ring of a curve over a number field k relative to its representation in SLn(k), and relate this to the study of K2 of the curve.
متن کاملRELATIVE PRO-l COMPLETIONS OF MAPPING CLASS GROUPS
Fix a prime number l. In this paper we develop the theory of relative pro-l completion of discrete and profinite groups — a natural generalization of the classical notion of pro-l completion — and show that the pro-l completion of the Torelli group does not inject into the relative pro-l completion of the corresponding mapping class group when the genus is at least 2. (See Theorem 1 below.) As ...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2004
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2004.01.011