Summary
By means of Adams operations in algebraic K-theory we study the order of differentials in the Brown-Gersten-Quillen spectral sequence for a scheme.
2010 Mathematics subject classification. 14C35, 19E08, 19L20.
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References
J. F. Adams, Lectures on generalised cohomology, Category Theory, Homology Theory and their Applications, III (Battelle Institute Conference, Seattle, Wash., 1968, Vol. Three), Springer, Berlin, 1969, pp. 1–138.
E. Friedlander and A. Suslin, The spectral sequence relating algebraic K-theory to motivic cohomology, Ann. Sci. École Norm. Sup. (4) 35 (2002), no. 6, 773–875.
H. Gillet, Riemann-Roch theorems for higher algebraic K-theory, Adv. in Math. 40 (1981), no. 3, 203–289.
H. L. Hiller, λ-rings and algebraic K-theory, J. Pure Appl. Algebra 20 (1981), no. 3, 241–266.
Ch. Kratzer, λ-structure en K-théorie algébrique, Comment. Math. Helv. 55 (1980), no. 2, 233–254.
Ch. Kratzer-, Opérations d’Adams et représentations de groupes, Enseign. Math. (2) 26 (1980), no. 1–2, 141–154.
M. Levine, K-theory and motivic cohomology of schemes, http://www.math.uiuc.edu/K-theory/0336/ (1999).
A. S. Merkurjev and A. A. Suslin, K-cohomology of Severi-Brauer varieties and the norm residue homomorphism, Izv. Akad. Nauk SSSR Ser. Mat. 46 (1982), no. 5, 1011–1046, 1135–1136.
I. Panin, Riemann-Roch theorems for oriented cohomology, Axiomatic, enriched and motivic homotopy theory, NATO Sci. Ser. II Math. Phys. Chem., vol. 131, Kluwer Acadamic Publisher, Dordrecht, 2004, pp. 261–333.
D. Quillen, Higher algebraic K-theory. I, (1973), 85–147. Lecture Notes in Math., Vol. 341.
C. Soulé, Opérations en K-théorie algébrique, Can. J. Math. 37 (1985), no. 3, 488–550.
V. Voevodsky, A. Suslin, and E. Friedlander, Cycles, transfers, and motivic homology theories, Princeton University Press, Princeton, NJ, 2000.
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Merkurjev, A. (2010). Adams Operations and the Brown-Gersten-Quillen Spectral Sequence. In: Colliot-Thélène, JL., Garibaldi, S., Sujatha, R., Suresh, V. (eds) Quadratic Forms, Linear Algebraic Groups, and Cohomology. Developments in Mathematics, vol 18. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6211-9_19
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DOI: https://doi.org/10.1007/978-1-4419-6211-9_19
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