Motivic Cohomology of Groups of Order p^3

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dc.contributor.advisorBrosnan, Patricken_US
dc.contributor.authorBlack, Rebeccaen_US
dc.contributor.departmentMathematicsen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2018-09-15T05:37:03Z
dc.date.available2018-09-15T05:37:03Z
dc.date.issued2018en_US
dc.description.abstractIn this thesis we compute the motivic cohomology ring (also known as Bloch's higher Chow groups) with finite coefficients for the two nonabelian groups of order $27$, thought of as affine algebraic groups over $\mathbb{C}$. Specifically, letting $\tau$ denote a generator of the motivic cohomology group $H^{0,1}(BG,\Z/3) \cong \Z/3$ where $G$ is one of these groups, we show that the motivic cohomology ring contains no $\tau$-torsion, and so can be computed as a weight filtration on the ordinary group cohomology. In the case of a prime $p > 3$, there are also two nonabelian groups of order $p^3$. We make progress toward computing the motivic cohomology in the general case as well by reducing the question to understanding the $\tau$-torsion on the motivic cohomology of a $p$-dimensional variety; we also compute the motivic cohomology of $BG$ for general $p$ modulo the $\tau$-torsion classes.en_US
dc.identifierhttps://doi.org/10.13016/M2TM7246G
dc.identifier.urihttp://hdl.handle.net/1903/21406
dc.language.isoenen_US
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pquncontrolledalgebraic geometryen_US
dc.subject.pquncontrolledchow groupsen_US
dc.subject.pquncontrolledmotivic cohomologyen_US
dc.titleMotivic Cohomology of Groups of Order p^3en_US
dc.typeDissertationen_US

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