关于赋值模
On modules over valuations
摘要：
最近，光滑赋值代数被附加到任何光滑流形上。粗略地说，一个光滑赋值是紧致角子流形上满足一些额外性质的可加测度。本文主要研究光滑赋值上的模。更具体地说，我们研究了仿射生成的投射模在类似的研究向量丛的流形。特别地，证明了在紧致流形上，由赋值上的n-生成投射模构造的$K$ -环与由向量丛构造的经典拓扑$K^0$ -环之间存在典范同构.
英文摘要：
Recently an algebra of smooth valuations was attached to any smooth manifold. Roughly put, a smooth valuation is finitely additive measure on compact submanifolds with corners which satisfies some extra properties. In this note we initiate a study of modules over smooth valuations. More specifically we study finitely generated projective modules in analogy to the study of vector bundles on a manifold. In particular it is shown that on a compact manifold there exists a canonical isomorphism between the $K$-ring constructed out of finitely generated projective modules over valuations and the classical topological $K^0$-ring constructed out of vector bundles.
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