Hokkaido Mathematical Journal

Algebraic BP-theory and norm varieties

Nobuaki YAGITA

Abstract

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.

Article information

Source
Hokkaido Math. J., Volume 41, Number 2 (2012), 275-316.

Dates
First available in Project Euclid: 26 June 2012

https://projecteuclid.org/euclid.hokmj/1340714416

Digital Object Identifier
doi:10.14492/hokmj/1340714416

Mathematical Reviews number (MathSciNet)
MR2977048

Zentralblatt MATH identifier
1321.14005

Citation

YAGITA, Nobuaki. Algebraic BP -theory and norm varieties. Hokkaido Math. J. 41 (2012), no. 2, 275--316. doi:10.14492/hokmj/1340714416. https://projecteuclid.org/euclid.hokmj/1340714416