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Journal of K-Theory (1)

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On a local to global principle in étale K-groups of curves
Grzegorz Banaszak, Piotr Krasoń
Journal:

Journal of K-Theory / Volume 12 / Issue 1 / August 2013

Published online by Cambridge University Press:

17 May 2013, pp. 183-201

Print publication:

August 2013
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Let X be a smooth, proper and geometrically irreducible curve X defined over a number field F and let χ be a regular and proper model of X over OF,Sl. In this paper we address the problem of detecting the linear dependence over ℤl of elements in the étale K-theory of χ. To be more specific, let P ∊ Ket2n(χ) and let ⋀̂ ⊂ Ket2n(χ) be a ℤl-submodule. Let rυ: Ket2n(χ) → Ket2n(χυ) be the reduction map for υ ∉ Sl. We prove, under some conditions on X, that if rυ() ∈ rυ (⋀̂) for almost all υ of then ∈ ⋀̂ + Ket2n(χ)tor.