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Bulletin of the London Mathematical Society Advance Access originally published online on March 31, 2008
Bulletin of the London Mathematical Society 2008 40(2):263-273; doi:10.1112/blms/bdn006
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© 2008 London Mathematical Society

Jaffard–Ohm correspondence and Hochster duality

Wolfgang Rump and Yi Chuan Yang

Institut für Algebra und Zahlentheorie
Universität Stuttgart
Pfaffenwaldring 57
D-70550 Stuttgart
Germany
ycyang@buaa.edu.cn

Received 19 January 2007. Revision received 11 October 2007.

We study categorical aspects of the Jaffard–Ohm correspondence between abelian l-groups and Bézout domains and show that this correspondence is close to a localization. For this purpose, we establish a general extension theorem for valuations with value group that is an abelian l-group. As an application, we prove Anderson's conjecture which refines the Jaffard–Ohm correspondence. We then extend the correspondence to sheaves on spectral spaces and show that the spectrum of a Bézout domain and the spectrum of its corresponding abelian l-group provide a concrete example for Hochster's duality of spectral spaces.

Dedicated to B.V.M.

2000 Mathematics Subject Classification 13A05, 13G05, 06F20, 13A18 (primary), 14A05 (secondary).


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