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

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


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


Zbl 0292.18004
Full Text: DOI EuDML


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