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# Chow Motives of Del Pezzo Surfaces of Degree 5 and 6 Open Access

## Descriptions

Other title
Subject/Keyword

Type of item
Thesis
Degree grantor
University of Alberta
Author or creator
Helmsauer, Kathrin S M
Supervisor and department
Gille, Stefan (Mathematical and Statistical Sciences)
Examining committee member and department
Gille, Stefan (Mathematical and Statistical Sciences)
Lewis, James (Mathematical and Statistical Sciences)
Guay, Nicolas (Mathematical and Statistical Sciences)
Chernousov, Vladimir (Mathematical and Staistical Sciences)
Putkaradze, Vakhtang (Mathematical and Statistical Sciences)
Department
Department of Mathematical and Statistical Sciences
Specialization
Mathematics
Date accepted
2013-09-17T14:36:39Z
2013-11
Degree
Master of Science
Degree level
Master's
Abstract
We determine the decomposition of the Chow motive of a Del Pezzo surface $S$ of degree 5 or 6 with a $K$-rational point $\mathrm{pt}:K\rightarrow S$ into a direct sum of Chow motives. In each case, we give a $\operatorname{Gal}\left( \overline K/K\right)$-permutation resolution of the Picard group $\pic \left( \overline K \times_K S \right)$ and deduce that there is some étale algebra $E$ such that the corresponding twisted motive $\left( \spec E, \id_{\spec E} \right)(1)$ is isomorphic to the direct sum of $\left( S,\id_S - (\mathrm{pt} \times S + S\times \mathrm{pt}) \right)$ and $\left( \spec K, \id_{\spec K} \right) (1)$.
Language
English
DOI
doi:10.7939/R3RN30G71
Rights
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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