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)...
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| Main Author: | |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
31 May 2018
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| In: |
Advances in mathematics
Year: 2018, Volume: 333, Pages: 314-349 |
| ISSN: | 1090-2082 |
| DOI: | 10.1016/j.aim.2018.05.034 |
| Online Access: | 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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| Author Notes: | Pavel Sechin |
| Summary: | 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. |
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| Item Description: | Gesehen am 06.03.2019 |
| Physical Description: | Online Resource |
| ISSN: | 1090-2082 |
| DOI: | 10.1016/j.aim.2018.05.034 |