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An Elementary Proof of Suslin Reciprocity

Published online by Cambridge University Press:  20 November 2018

Matt Kerr
Matt Kerr*
Affiliation:
Department of Mathematics, Box 951555, 5436 MSB, UCLA, Los Angeles, CA 90095-1555, U.S.A. e-mail: [email protected]
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Abstract

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We state and prove an important special case of Suslin reciprocity that has found significant use in the study of algebraic cycles. An introductory account is provided of the regulator and norm maps on Milnor ${{K}_{2}}$-groups (for function fields) employed in the proof.

Keywords

19D4519E15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 48 , Issue 2 , 01 June 2005 , pp. 221 - 236
Copyright
Copyright © Canadian Mathematical Society 2005

References

[BT] Bass, H. and Tate, J., The Milnor ring of a global field. In: Algebraic K-Theory, II. Lecture Notes in Mathematics 342, Springer-Verlag, New York, 1973, pp. 349–446.Google Scholar
[Bl] Bloch, S., Algebraic cycles and higher K-theory. Adv. in Math. 61(1986), 267–304.Google Scholar
[GG1] Green, M. and Griffiths, P., On the tangent space to the space of algebraic cycles on a smooth algebraic variety. Preprint, 2002.Google Scholar
[GG2] Green, M. and Griffiths, P., correspondence, 1999.Google Scholar
[GH] Griffiths, P. and Harris, J., Principles of Algebraic Geometry. John Wiley, New York, 1978.Google Scholar
[Ha] Hain, R., Classical Polylogarithms. In: Motives (Seattle, WA, 1991), Proceedings Sympos. Pure Math., Amererican Mathematical Society, Providence, RI, 1994, pp. 3–42.Google Scholar
[K] Kerr, M., Geometric constrcution of regulator currents with applications to algebraic cycles, Princeton thesis, 2003.Google Scholar
[L] Lewis, J., A filtration on the Chow groups of a complex projective variety, Compositio Math. 128(2001), 299–322.Google Scholar
[So] Somekawa, M., On Milnor K-groups attached to semi-abelian varieties. K-Theory 4(1990), 105–119.Google Scholar
[S1] Suslin, A., Reciprocity laws and the stable rank of rings of polynomials. (Russian), Izv. Akad. Nauk SSSR Ser. Mat. 43(1979), 1394–1429.Google Scholar
[S2] Suslin, A., Algebraic K-theory of fields. Proc. ICM(1986), pp. 222–244.Google Scholar
[T] Totaro, B., Milnor K-theory is the simplest part of algebraic K-theory. K-Theory 6(1992), 177–189.Google Scholar