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dc.contributor.authorQuick, Gereon
dc.contributor.authorStrand, Therese
dc.contributor.authorWilson, Glen Matthew
dc.date.accessioned2023-02-15T14:57:03Z
dc.date.available2023-02-15T14:57:03Z
dc.date.issued2022-02-24
dc.description.abstractWe study which quadratic forms are representable as the local degree of a map f:An→An with an isolated zero at 0 , following the work of Kass and Wickelgren who established the connection to the quadratic form of Eisenbud, Khimshiashvili, and Levine. Our main observation is that over some base fields k , not all quadratic forms are representable as a local degree. Empirically the local degree of a map f:An→An has many hyperbolic summands, and we prove that in fact this is the case for local degrees of low rank. We establish a complete classification of the quadratic forms of rank at most 7 that are representable as the local degree of a map over all base fields of characteristic different from 2 . The number of hyperbolic summands was also studied by Eisenbud and Levine, where they establish general bounds on the number of hyperbolic forms that must appear in a quadratic form that is representable as a local degree. Our proof method is elementary and constructive in the case of rank 5 local degrees, while the work of Eisenbud and Levine is more general. We provide further families of examples that verify that the bounds of Eisenbud and Levine are tight in several cases.en_US
dc.identifier.citationQuick G, Strand T, Wilson GM. Representability of the local motivic Brouwer degree. Mathematica Scandinavica. 2022;128(1):54-77en_US
dc.identifier.cristinIDFRIDAID 2005917
dc.identifier.doi10.7146/math.scand.a-129287
dc.identifier.issn0025-5521
dc.identifier.issn1903-1807
dc.identifier.urihttps://hdl.handle.net/10037/28569
dc.language.isoengen_US
dc.publisherMathematica Scandinavicaen_US
dc.relation.journalMathematica Scandinavica
dc.relation.projectIDNorges forskningsråd: 313472en_US
dc.rights.accessRightsopenAccessen_US
dc.rights.holderCopyright 2022 The Author(s)en_US
dc.rights.urihttps://creativecommons.org/licenses/by/4.0en_US
dc.rightsAttribution 4.0 International (CC BY 4.0)en_US
dc.titleRepresentability of the local motivic Brouwer degreeen_US
dc.type.versionacceptedVersionen_US
dc.typeJournal articleen_US
dc.typeTidsskriftartikkelen_US
dc.typePeer revieweden_US


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Attribution 4.0 International (CC BY 4.0)
Except where otherwise noted, this item's license is described as Attribution 4.0 International (CC BY 4.0)