Factor Equivalence of Rings of Integers and Chinburg's Invariant in the Defect Class Group

Holland, D.; Wilson, S. M. J.

doi:10.1112/jlms/49.3.417

Cited by 5 publications

(16 citation statements)

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“…Moreover, it is interesting to observe that our proof of Corollary 7.8 is by no means a direct re®nement of the arguments of [24]. Indeed, by systematically working with relative K-groups and using functoriality considerations, we have avoided any use of the theory of factorisability defect class groups' which is developed in [23] and is central to the proofs of [25,24].…”

Section: Functorial Behaviourmentioning

confidence: 99%

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Equivariant Epsilon Constants, Discriminants and Étale Cohomology

Bley

Burns

2003

Proc. London Math. Soc.

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Section: Functorial Behaviourmentioning

confidence: 99%

“…cit. In particular, we completely avoid any reference to the theory of`factorisability defect class groups' which was developed in [23] and is central to the computations of [25,24].…”

Section: Introductionmentioning

confidence: 99%

Equivariant Epsilon Constants, Discriminants and Étale Cohomology

Bley

Burns

2003

Proc. London Math. Soc.

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“…Latterly (see e.g. [7]) it has been shown that such theories can also produce useful information on the global aspects of the relationships between M and N (i.e. aspects which depend on more than just the genera of N and M ).…”

Section: Introductionmentioning

confidence: 99%

“…The main purposes this paper are 1. to give (Section 3) a general, uniform, framework for the description of factorizability theories (or, to be more precise, for the description of those factorizability theories which are aimed at the comparison of module structure) so that such theories may be compared (Section 4); 2. to place various existing theories (in particular those of [4] and of [7]) in this framework and to demonstrate their equivalence (10•1); 3. to develop the theory of the class group associated to such a factorizability theory (3•9, 3•11, 3•14). We also include a result (4•3 (ii)) on 'shadowing' of a similar nature to that considered in [4].…”

Section: Introductionmentioning

confidence: 99%

“…The methods of [7] involve the construction of a defect Grothendieck group where, loosely speaking, relations from short exact sequences are imposed but moderated by certain properties (exactness defects) of the exact sequences. In a later paper [8] we shall expose the relationships between factorizability theories and exactness defects and between factor equivalence and the defect class groups.…”

Section: Introductionmentioning

confidence: 99%

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Equivalence of factorizability theories

Wilson

1998

Math. Proc. Camb. Phil. Soc.

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A framework is given for defining and comparing factorizability theories (as used, for example, to relate modules over the group rings of finite groups). The strict theory of Fröhlich [4] and the Hecke theory of [7] as well as several other related theories are shown to be equivalent. Of particular interest among the several equivalent theories examined is that of normaliser factorizability. This is perhaps the most user friendly theory and follows most closely the framework of the classical theory. Among other tools, the theory of permutation projectives and their species is used.

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Localization and class groups of module categories with exactness defects

Holland

Wilson

1993

Math. Proc. Camb. Phil. Soc.

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We present a new way of forming a grothendieck group with respect to exact sequences. A ‘defect’ is attached to each non-split sequence and the relation that would normally be derived from a collection of exact sequences is only effective if the (signed) sum of the corresponding defects is zero. The theory of the localization exact sequence and, in particular, of the relative group in this sequence is developed. The (‘locally free’) class group of a module category with exactness defect is defined and an idèlic formula for this is given. The role of torsion and of torsion-free modules is investigated. One aim of the work is to enhance the locally trivial, ‘class group’, invariants obtainable for a module while keeping to a minimum the local obstructions to the definition of such invariants.

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Factor Equivalence of Rings of Integers and Chinburg's Invariant in the Defect Class Group

Cited by 5 publications

References 0 publications

Equivariant Epsilon Constants, Discriminants and Étale Cohomology

Equivariant Epsilon Constants, Discriminants and Étale Cohomology

Equivalence of factorizability theories

Localization and class groups of module categories with exactness defects

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