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The Reduction of an RG–Lattice Modulo pn

Published online by Cambridge University Press:  20 November 2018

Peter Symonds
Peter Symonds*
Affiliation:
McMaster University, Hamilton, Ontario
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We define the cover of an RG-module V to consist of an RG lattice Ṽ and a homomorphism π : Ṽ→ V such that π induces an isomorphism on Ext*RG(M, —) for any RG-lattice M. Here G is a finite group and, for simplicity in this introduction, R is a complete discrete valuation ring of characteristic zero with prime element p and perfect valuation class field. Let pn(G) be the highest power of p that divides |G| and, given an RG-lattice M, let pn(M) be the smallest power of p such that pn(M) idM : M→M factors through a projective lattice: n(M)≦n(G).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 2 , 01 April 1990 , pp. 342 - 364
Copyright
Copyright © Canadian Mathematical Society 1990

References

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