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An Arithmetic Analogue of Bezout's Theorem

Published online by Cambridge University Press:  04 December 2007

David McKinnon
Affiliation:
Mathematics Department, Bromfield-Pearson Hall, Tufts University, Medford, MA 02155, U.S.A.
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Abstract

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In this paper, we prove two versions of an arithmetic analogue of Bezout's theorem, subject to some technical restrictions. The basic formula proven is deg(V)h(XY)=h(X)deg(Y)+h(Y)deg(X)+O(1), where X and Y are algebraic cycles varying in properly intersecting families on a regular subvariety VSPSN. The theorem is inspired by the arithmetic Bezout inequality of Bost, Gillet, and Soulé, but improve upon it in two ways. First, we obtain an equality up to O(1) as the intersecting cycles vary in projective families. Second, we generalise this result to intersections of divisors on any regular projective arithmetic variety.

Type
Research Article
Copyright
© 2001 Kluwer Academic Publishers