United Elliptic Homology
United Elliptic Homology
View/Type of Scholarly Publication
DissertationDate of Exam
22.08.2012Date of Publication
11.09.2012Advisor
Schwede, StefanCo-Referee
Laures, GerdMetadata
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Abstract
We study the categories of modules over real K-theory and TMF. Inspired by work of Bousfield, we consider TMF-modules at the prime 3 which are relatively free with respect to TMF(2). We show that a large class of these can be iteratively built from TMF by coning off torsion elements and killing generators. This is based on a detailed study of vector bundles on the moduli stack of elliptic curves. Furthermore, we consider examples of TMF-modules and show that the categories of TMF-modules and quasi-coherent sheaves on the derived moduli stack of elliptic curves are equivalent (at primes bigger than 2).
Subjects
Elliptische Kohomologie, stabile Homotopietheorie, Vektorbündel, topologische Modulformen, Elliptic cohomology, Stable homotopy theory, Vector Bundles, Topological modular forms
Classification (DDC)
510 MathematikMeier, Lennart: United Elliptic Homology. - Bonn, 2012. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-29694
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5n-29694
@phdthesis{handle:20.500.11811/5378,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-29694,
author = {{Lennart Meier}},
title = {United Elliptic Homology},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2012,
month = sep,
note = {We study the categories of modules over real K-theory and TMF. Inspired by work of Bousfield, we consider TMF-modules at the prime 3 which are relatively free with respect to TMF(2). We show that a large class of these can be iteratively built from TMF by coning off torsion elements and killing generators. This is based on a detailed study of vector bundles on the moduli stack of elliptic curves. Furthermore, we consider examples of TMF-modules and show that the categories of TMF-modules and quasi-coherent sheaves on the derived moduli stack of elliptic curves are equivalent (at primes bigger than 2).},
url = {https://hdl.handle.net/20.500.11811/5378}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5n-29694,
author = {{Lennart Meier}},
title = {United Elliptic Homology},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2012,
month = sep,
note = {We study the categories of modules over real K-theory and TMF. Inspired by work of Bousfield, we consider TMF-modules at the prime 3 which are relatively free with respect to TMF(2). We show that a large class of these can be iteratively built from TMF by coning off torsion elements and killing generators. This is based on a detailed study of vector bundles on the moduli stack of elliptic curves. Furthermore, we consider examples of TMF-modules and show that the categories of TMF-modules and quasi-coherent sheaves on the derived moduli stack of elliptic curves are equivalent (at primes bigger than 2).},
url = {https://hdl.handle.net/20.500.11811/5378}
}
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