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Grayson, Daniel R.

Projections, cycles, and algebraic \(K\)-theory. (English) Zbl 0358.18012

Math. Ann. 234, 69-72 (1978).
A theorem of D. Quillen [Theorem 5.11, Sect. 7, Higher Algebraic K-theory I, Lecture Notes Math. 341, 85–147 (1973; Zbl 0292.18004)] known as Gersten’s conjecture, the main step in the proof of Bloch’s formula for the group of cycles modulo rational equivalence on a non-singular variety, is proved in a different way. The difference consists of the use of linear projections in place of arbitrary ones. When the ground field is infinite a suitably chosen linear projection serves to prove the theorem. A trick of J. Roberts is used to extend the result to cover the case of a finite ground field.
Reviewer: Daniel R. Grayson
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Cited in 8 Documents

MSC:

18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)

Citations:

Zbl 0292.18004
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\textit{D. R. Grayson}, Math. Ann. 234, 69--72 (1978; Zbl 0358.18012)
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References:

[1] Grothendieck,A., Dieudonné,J.A.: Eléments de géométrie algébrique. EGA IV. Publications Mathématiques, IHES No. 20, 24, 28, 32, Paris, 1964, 65, 66, 67
[2] Grothendieck, A.: Revetements étales et groupe fondamental. SGA 1. Lecture Notes in Mathematics 224. Berlin, Heidelberg, New York: Springer 1971 · Zbl 0234.14002
[3] Quillen, D.: Higher algebraicK-theory. II. In: AlgebraicK-theory I. Lecture Notes in Mathematics 341. Berlin, Heidelberg, New York: Springer 1973 · Zbl 0292.18004
[4] Roberts, J.: Chow’s moving lemma. In: Algebraic geometry, Oslo 1970, ed. by F. Oort. Groningen: Wolters-Noordhoff 1972
[5] Shafarevich, I.: Basic algebraic geometry. Berlin, Heidelberg, New York: Springer 1974 · Zbl 0284.14001
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