K. Zainoulline: A Purity Theorem for Functors with Transfers


Submission: 2000 Apr. 07

Let $R$ be a local regular ring of geometric type and $K$ be its field of fractions. Let $\f$ be a covariant functor from the category of $R$-algebras to abelian groups satisfying some additional properties (continuity, existence of well behaving transfer map). We show that the following equality holds for the subgroups of the group $\f(K)$: $$ \bigcap_{\p\in\spec R, ht\p=1}\im\{\f(R_\p)\ra\f(K)\}= \im\{\f(R)\ra \f(K)\}, $$ where all maps are induced by the canonical inclusions.

1991 Mathematics Subject Classification:

Keywords and Phrases:

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