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Jaffard–Ohm correspondence and Hochster duality
Author(s) -
Rump Wolfgang,
Yang Yi Chuan
Publication year - 2008
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdn006
Subject(s) - duality (order theory) , mathematics , ohm , dual (grammatical number) , mathematical economics , calculus (dental) , pure mathematics , electrical engineering , philosophy , medicine , engineering , linguistics , dentistry
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.