Intersection theory using Adams operations. (English) Zbl 0632.14009

The \(\lambda\)-structure of algebraic K-theory with supports is used to prove three results on intersection theory. The first result is a vanishing theorem for intersection multiplicities which was conjectured by Serre who proved it in several cases; another proof was obtained by Roberts. The second result describes, in positive characteristic, the action of the Frobenius endomorphism on the Euler characteristic of a complex; it is a special case of a conjecture by Szpiro. Finally, a multiplicative structure on the Chow groups of any noetherian regular scheme, after tensoring these by \({\mathbb{Q}}\) is introduced.
Reviewer: L.Vaserstein


14C35 Applications of methods of algebraic \(K\)-theory in algebraic geometry
14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry
18F25 Algebraic \(K\)-theory and \(L\)-theory (category-theoretic aspects)
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