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dc.contributor.author
Kratsios, Anastasis
dc.date.accessioned
2021-03-04T10:51:11Z
dc.date.available
2021-02-15T05:50:10Z
dc.date.available
2021-02-15T09:45:01Z
dc.date.available
2021-03-04T10:51:11Z
dc.date.issued
2021-02
dc.identifier.other
10.3390/math9030251
en_US
dc.identifier.uri
http://hdl.handle.net/20.500.11850/469365
dc.identifier.doi
10.3929/ethz-b-000469365
dc.description.abstract
The Hochschild cohomological dimension of any commutative k-algebra is lower-bounded by the least-upper bound of the flat-dimension difference and its global dimension. Our result is used to show that for a smooth affine scheme X satisfying Pointcaré duality, there must exist a vector bundle with section M and suitable n which the module of algebraic differential n-forms Ωn(X,M). Further restricting the notion of smoothness, we use our result to show that most k-algebras fail to be smooth in the quasi-free sense. This consequence, extends the currently known results, which are restricted to the case where k=C.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
MDPI
en_US
dc.rights.uri
http://creativecommons.org/licenses/by/4.0/
dc.subject
hochschild cohomology
en_US
dc.subject
homological dimension theory
en_US
dc.subject
non-commutative geometry
en_US
dc.subject
quasi-free algebras
en_US
dc.subject
pointcaré duality
en_US
dc.subject
higher differential forms
en_US
dc.title
Lower-estimates on the hochschild (Co)homological dimension of commutative algebras and applications to smooth affine schemes and quasi-free algebras
en_US
dc.type
Journal Article
dc.rights.license
Creative Commons Attribution 4.0 International
dc.date.published
2021-01-27
ethz.journal.title
Mathematics
ethz.journal.volume
9
en_US
ethz.journal.issue
3
en_US
ethz.pages.start
251
en_US
ethz.size
22 p.
en_US
ethz.version.deposit
publishedVersion
en_US
ethz.identifier.wos
ethz.identifier.scopus
ethz.publication.place
Basel
en_US
ethz.publication.status
published
en_US
ethz.date.deposited
2021-02-15T05:50:15Z
ethz.source
SCOPUS
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2021-02-15T09:45:12Z
ethz.rosetta.lastUpdated
2022-03-29T05:37:12Z
ethz.rosetta.versionExported
true
ethz.COinS
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