UMD Theses and Dissertations

Permanent URI for this collectionhttp://hdl.handle.net/1903/3

New submissions to the thesis/dissertation collections are added automatically as they are received from the Graduate School. Currently, the Graduate School deposits all theses and dissertations from a given semester after the official graduation date. This means that there may be up to a 4 month delay in the appearance of a given thesis/dissertation in DRUM.

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Author: search.filters.author.Black, Rebecca

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    Motivic Cohomology of Groups of Order p^3
    (2018) Black, Rebecca; Brosnan, Patrick; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)
    In 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.