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Algebraic cobordisms of a Pfister quadric
Author(s) -
Vishik A.,
Yagita N.
Publication year - 2007
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdm056
Subject(s) - quadric , mathematics , homomorphism , injective function , algebraic number , pure mathematics , ring (chemistry) , field (mathematics) , variety (cybernetics) , extension (predicate logic) , computation , algebra over a field , computer science , mathematical analysis , statistics , algorithm , chemistry , organic chemistry , programming language
In this article we compute the ring of algebraic cobordisms of a Pfister quadric. This is a rare example of a non‐cellular variety where such a computation is known. We consider the algebraic cobordisms Ω* of Levine and Morel, as well as the MGL 2*, * of Voevodsky. The methods of computation in these two cases are quite different. However, the results do agree (which supports the expectation that the two theories actually coincide). We show that the restriction homomorphism in our case is injective for any field extension E / F .