Projections, cycles, and algebraic \(K\)-theory (Q1239249)

A theorem of \textit{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 \textit{J. Roberts} is used to extend the result to cover the case of a finite ground field.