On the structure of algebraic cobordism
In this paper we investigate the structure of algebraic cobordism of Levine-Morel as a module over the Lazard ring with the action of Landweber-Novikov and symmetric operations on it. We show that the associated graded groups of algebraic cobordism with respect to the topological filtration Ω(r)⁎(X)...
Gespeichert in:
| 1. Verfasser: | |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
31 May 2018
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| In: |
Advances in mathematics
Year: 2018, Jahrgang: 333, Pages: 314-349 |
| ISSN: | 1090-2082 |
| DOI: | 10.1016/j.aim.2018.05.034 |
| Online-Zugang: | Resolving-System, Volltext: http://dx.doi.org/10.1016/j.aim.2018.05.034 Verlag, Volltext: http://www.sciencedirect.com/science/article/pii/S0001870818302093 
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| Verfasserangaben: | Pavel Sechin |
MARC
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| 520 | |a In this paper we investigate the structure of algebraic cobordism of Levine-Morel as a module over the Lazard ring with the action of Landweber-Novikov and symmetric operations on it. We show that the associated graded groups of algebraic cobordism with respect to the topological filtration Ω(r)⁎(X) are unions of finitely presented L-modules of very specific structure. Namely, these submodules possess a filtration such that the corresponding factors are either free or isomorphic to cyclic modules L/I(p,n)x where degx≥pn−1p−1. As a corollary we prove the Syzygies Conjecture of Vishik on the existence of certain free L-resolutions of Ω⁎(X), and show that algebraic cobordism of a smooth surface can be described in terms of K0 together with a topological filtration. | ||
| 650 | 4 | |a Algebraic cobordism | |
| 650 | 4 | |a Landweber's filtration | |
| 650 | 4 | |a Symmetric operations | |
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