1,347,748 research outputs found
Maps between local Picard groups
We study the local Picard group of singularities. We study those elements in
the local Picard group that become trivial either when pulled-back to the
normalization or when restricted to a hyperplane section. In the second case we
improve the similar results of SGA2. Version2: Many small changes, new Theorem
4 added
Local units versus local projectivity. Dualisations: Corings with local structure maps
We unify and generalize different notions of local units and local
projectivity. We investigate the connection between these properties by
constructing elementary algebras from locally projective modules. Dual versions
of these constructions are discussed, leading to corings with local
comultiplications, corings with local counits and rings with local
multiplications.Comment: 22 pages, including a correction to Proposition 1.
A New Method of Extension of Local Maps of Banach Spaces. Applications and Examples
A known classical method of extension of smooth local maps of Banach spaces
uses smooth bump functions. However, such functions are absent in the majority
of infinite-dimensional Banach spaces. This is an obstacle in the development
of local analysis, in particular in the questions of extending local maps onto
the whole space. We suggest an approach that substitutes bump functions with
special maps, which we call blid maps. It allows us to extend smooth local maps
from non-smooth spaces, such as . As an example of
applications, we show how to reconstruct a map from its derivatives at a point,
for spaces possessing blid maps. We also show how blid maps can assist in
finding global solutions to cohomological equations having linear
transformation of argument.Comment: arXiv admin note: substantial text overlap with arXiv:1703.0629
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