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Brauer Groups, Class Groups and Maximal Orders for a Krull Scheme

Published online by Cambridge University Press:  20 November 2018

Heisook Lee  and
Morris Orzech
Heisook Lee
Affiliation:
Ewha Woman's University, Seoul, South Korea
Morris Orzech
Affiliation:
Ewha Woman's University, Seoul, South Korea
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In a previous paper [13] one of us considered Brauer groups Br(C) and class groups Cl(C) attached to certain monoidal categories C of divisorial R-lattices. That paper showed that the groups arising for a suitable pair of categories C1 ⊆ C2 could be related by a tidy exact sequence

It was shown that this exact sequence specializes to a number of exact sequences which had formerly been handled separately. At the same time the conventional setting of noetherian normal domains was replaced by that of Krull domains, thus generalizing previous results while also simplifying the proofs. This work was carried out in an affine setting, and one aim of the present paper is to carry these results over to Krull schemes. This will enable us to recover the non-affine version of an exact sequence obtained by Auslander [1, p. 261], as well as to introduce a new, non-affine version of a different sequence derived by the same author [2, Theorem 1].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 34 , Issue 4 , 01 August 1982 , pp. 996 - 1010
Copyright
Copyright © Canadian Mathematical Society 1982

References

References>

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