Linear groups over local rings
نویسندگان
چکیده
منابع مشابه
Orthogonal Groups over Local Rings
In an earlier paper [S] we have determined the structure of the linear groups over a local ring. In this note we continue the study of the classical groups over a local ring with the investigation of the orthogonal groups. Our main result (cf. Theorem 6 below) is a complete description of the invariant subgroups of an orthogonal group of noncompact type (i.e., of index ^ 1) over a local ring L ...
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We prove that if R is a Hensel local ring with infinite residue field k, the natural map Hi(GLn(R),Z/p) → Hi(GLn(k), Z/p) is an isomorphism for i ≤ 3, p 6= char k. This implies rigidity for Hi(GLn), i ≤ 3, which in turn implies the Friedlander–Milnor conjecture in positive characteristic in degrees ≤ 3. A fundamental question in the homology of linear groups is that of rigidity: given a smooth ...
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For a discrete group G there are two well-known completions. The first is the Malcev (or unipotent) completion. This is a prounipotent group U , defined over Q, together with a homomorphism ψ : G → U that is universal among maps from G into prounipotent Q-groups. To construct U , it suffices to consider the case where G is nilpotent; the general case is handled by taking the inverse limit of th...
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We study the homology of SLn(F [t, t ]) by examining the action of the group on a suitable simplicial complex. The E–term of the resulting spectral sequence is computed and the differential, d, is calculated in some special cases to yield information about the low-dimensional homology groups of SLn(F [t, t ]). In particular, we show that if F is an infinite field, then H2(SLn(F [t, t ]), Z) = K...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1960
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1960-10477-6