Open Access
June 2012 Algebraic BP-theory and norm varieties
Nobuaki YAGITA
Hokkaido Math. J. 41(2): 275-316 (June 2012). DOI: 10.14492/hokmj/1340714416


Let p be an odd prime and BP*(pt) ≅ $¥mathbb Z$(p)[v1,v2,…] the coefficient ring of the Brown-Peterson cohomology theory BP*(−) with |vi| = −2pi + 2. We study ABP*,*'(−) theory, which is the counter part in algebraic geometry of the BP*(−) theory. Let k be a field with k ⊂ $¥mathbb C$ and K*M(k) the Milnor K-theory. For a nonzero symbol aKn+1M(k)/p, a norm variety Va is a smooth variety such that a|k(Va) = 0 ∈ Kn+1M(k(Va))/p and V a($¥mathbb C$) = vn. In particular, we compute ABP*,*'(Ma) for the Rost motive Ma which is a direct summand of the motive M(Va) of some norm variety Va.


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Nobuaki YAGITA. "Algebraic BP-theory and norm varieties." Hokkaido Math. J. 41 (2) 275 - 316, June 2012.


Published: June 2012
First available in Project Euclid: 26 June 2012

zbMATH: 1321.14005
MathSciNet: MR2977048
Digital Object Identifier: 10.14492/hokmj/1340714416

Primary: 14C15 , 57T25
Secondary: 55R35 , 57T05

Keywords: algebraic cobordism , BP-theory , norm variety

Rights: Copyright © 2012 Hokkaido University, Department of Mathematics

Vol.41 • No. 2 • June 2012
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