Sheaves with finitely generated isomorphic stalks and homology manifolds

Authors:
Jerzy Dydak and John Walsh

Journal:
Proc. Amer. Math. Soc. **103** (1988), 655-660

MSC:
Primary 57P05; Secondary 18F20, 54B40

MathSciNet review:
943100

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Abstract: The setting is sheaves of modules over a commutative ring . It is shown that on completely metrizable spaces certain sheaves having mutually isomorphic finitely generated stalks are locally constant over a dense open subset. This is used to show that a locally compact metrizable space that is homologically locally connected with respect to a principal ideal domain is a homology manifold over provided it has finite cohomological dimension with respect to and, for any two points , the modules and are isomorphic and finitely generated.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1988-0943100-4

Keywords:
Homology manifold,
sheaf

Article copyright:
© Copyright 1988
American Mathematical Society