From algebraic cobordism to motivic cohomology

By Marc Hoyois. 2012

128 citations recorded by the source corpus.

Let S be an essentially smooth scheme over a eld of characteristic exponent c. We prove that there is a canonical equivalence of motivic spectra over S MGL=(a1;a2;::: )(1=c)' HZ(1=c); where HZ is the motivic cohomology spectrum, MGL is the algebraic cobordism spectrum, and the elements an are generators of the Lazard ring. We discuss several applications including the computation of the slices of Z(1=c)-local Landweber exact motivic spectra and the convergence of the associated slice spectral sequences.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/33242bd6aeaeda7e0408911ab71513261386a7aa

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In Geometry and Topology

1. P. Ostvaer
2. Marc Hoyois
3. Bogdan Gheorghe
4. Zhouli Xu
5. Shane Kelly
6. Guozhen Wang
7. O. Rondigs
8. M. Levine

In Mathematical Physics

1. P. Ostvaer
2. Bogdan Gheorghe
3. Zhouli Xu
4. Guozhen Wang
5. Marc Hoyois
6. Shane Kelly
7. O. Rondigs
8. M. Levine

Citations in the corpus

• The motivic Steenrod algebra in positive characteristic (2013, background): “ diagram (Xα) since it is unique as a proobject in the categoryofsmooth k-schemes[Gro66, Corollaire8.13.2]. Moreover, by [MVW06, Lemma 3.9], it is also independant of the choice of k. Theorem 4.24 in [Hoy13] shows that the motivic Eilenberg-Mac Lane spaces and spectra represent motivic cohomology: T”
• The special fiber of the motivic deformation of the stable homotopy category is algebraic (2018, background): “[25] Hoyois, M., From algebraic cobordism to motivic cohomology.”