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Motivic strict ring models for  -theory
Author(s):
Oliver
Röndigs;
Markus
Spitzweck;
Paul
Arne
Østvær
Journal:
Proc. Amer. Math. Soc.
138
(2010),
3509-3520.
MSC (2010):
Primary 14F42, 55P43;
Secondary 19E08
Posted:
May 10, 2010
MathSciNet review:
2661551
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Abstract:
It is shown that the  -theory of every noetherian base scheme of finite Krull dimension is represented by a commutative strict ring object in the setting of motivic stable homotopy theory. The adjective `strict' is used here in order to distinguish between the type of ring structure we construct and one which is valid only up to homotopy. An analogous topological result follows by running the same type of arguments as in the motivic setting.
References:
-
- 1.
- D.-C. Cisinski, F. Déglise.
Triangulated categories of motives.
arXiv:0912.2110. - 2.
- B. I. Dundas, O. Röndigs, P. A. Østvær.
Motivic functors.
Doc. Math. 8:489-525 (electronic), 2003. MR 2029171 (2004m:55011) - 3.
- D. Gepner, V. Snaith.
On the motivic spectra representing algebraic cobordism and algebraic  -theory.
Doc. Math. 14:359-396 (electronic), 2009. MR 2540697 - 4.
- J. F. Jardine.
Motivic symmetric spectra.
Doc. Math. 5:445-553 (electronic), 2000. MR 1787949 (2002b:55014) - 5.
- F. Morel, V. Voevodsky.
 -homotopy theory of schemes.
Inst. Hautes Études Sci. Publ. Math. 90:45-143 (2001), 1999. MR 1813224 (2002f:14029) - 6.
- N. Naumann, M. Spitzweck, P. A. Østvær.
Motivic Landweber exactness.
Doc. Math. 14:551-593 (electronic), 2009. - 7.
- N. Naumann, M. Spitzweck, P. A. Østvær.
Chern classes,  -theory and Landweber exactness over nonregular base schemes,
in Motives and Algebraic Cycles: A Celebration in Honour of Spencer J. Bloch, Fields Institute Communications, Vol. 56, 307-317, AMS, Providence, RI, 2009. - 8.
- I. Panin, K. Pimenov, O. Röndigs.
On Voevodsky's algebraic  -theory spectrum,
in Algebraic Topology, Abel Symposium 2007, 279-330, Springer-Verlag, Berlin, 2009. - 9.
- O. Röndigs, P. A. Østvær.
Motives and modules over motivic cohomology,
C. R. Math. Acad. Sci. 342:751-754, 2006. MR 2227753 (2007d:14043) - 10.
- O. Röndigs, P. A. Østvær.
Modules over motivic cohomology,
Adv. Math. 219:689-727, 2008. MR 2435654 (2009m:14026) - 11.
- S. Schwede.
An untitled book project about symmetric spectra.
Available on the author's homepage, http://www.math.uni-bonn.de/Tschwede. - 12.
- M. Spitzweck, P. A. Østvær.
The Bott inverted infinite projective space is homotopy algebraic  -theory,
Bull. London Math. Soc. 41:281-292, 2009. MR 2496504 - 13.
- M. Spitzweck, P. A. Østvær.
A Bott inverted model for equivariant unitary topological  -theory.
To appear in Math. Scand. - 14.
- V. Voevodsky.
 -homotopy theory.
In Proceedings of the International Congress of Mathematicians, Vol. I (Berlin, 1998), Vol. I: 579-604 (electronic), 1998. MR 1648048 (99j:14018)
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Additional Information:
Oliver
Röndigs
Affiliation:
Institut f{ür Mathematik, Universit{ät Osnabr{ück, 49069 Osnabrück, Germany
Email:
oroendig@math.uni-osnabrueck.de
Markus
Spitzweck
Affiliation:
Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, 0316 Oslo, Norway
Email:
markussp@math.uio.no
Paul
Arne
Østvær
Affiliation:
Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, 0316 Oslo, Norway
Email:
paularne@math.uio.no
DOI:
10.1090/S0002-9939-10-10394-3
PII:
S 0002-9939(10)10394-3
Received by editor(s):
October 13, 2009
Received by editor(s) in revised form:
January 19, 2010
Posted:
May 10, 2010
Communicated by:
Brooke Shipley
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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