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THE GEOMETRY OF MOTIVIC SPHERES
by
Adam Ericksen
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(MATHEMATICS)
Aug 2013
Copyright 2013 Adam Ericksen
Object Description
| Title | The geometry of motivic spheres |
| Author | Ericksen, Adam |
| Author email | aerickse@usc.edu;adamliniscus@gmail.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Mathematics |
| School | College of Letters, Arts And Sciences |
| Date defended/completed | 2013-05-24 |
| Date submitted | 2013-07-18 |
| Date approved | 2013-07-18 |
| Restricted until | 2013-07-18 |
| Date published | 2013-07-18 |
| Advisor (committee chair) | Asok, Aravind |
| Advisor (committee member) |
Friedlander, Eric M. Johnson, Clifford V. |
| Abstract | We study a class of smooth algebraic varieties which are, in the sense of Morel and Voevodsky's A¹-homotopy theory, homotopy equivalent to spheres. These varieties belong to a class of objects called vector bundle torsors, and we investigate their cohomological classification, and the isomorphism problem in general for them. In the affine case, we establish a criterion for non-isomorphy in terms of algebraic de Rham cohomology, as defined by Grothendieck. For all n ≥ 3, we then construct a pair of non-isomorphic smooth affine (2n-1)-dimensional varieties X and Y with the A¹-homotopy type of Aⁿ\0, with the property that X × Aⁿ⁻¹ ≃ Y × Aⁿ⁻¹. These results extend work of Dubouloz and Finston in the case n=2, and illustrate that motivic spheres of higher dimension exhibit non-cancellative behavior. |
| Keyword | motivic sphere; cancellation; A¹-homotopy theory |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m |
| Contributing entity | University of Southern California |
| Rights | Ericksen, Adam |
| Physical access | The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given. |
| Repository name | University of Southern California Digital Library |
| Repository address | USC Digital Library, University of Southern California, University Park Campus MC 7002, 106 University Village, Los Angeles, California 90089-7002, USA |
| Repository email | cisadmin@dots.usc.edu |
| Filename | etd-EricksenAd-1795.pdf |
| Archival file | uscthesesreloadpub_Volume3/etd-EricksenAd-1795.pdf |
Description
| Title | Page 1 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@dots.usc.edu |
| Full text | THE GEOMETRY OF MOTIVIC SPHERES by Adam Ericksen A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (MATHEMATICS) Aug 2013 Copyright 2013 Adam Ericksen |
