# PREPRINT 04/2000

K. Zainoulline

## A PURITY THEOREM FOR FUNCTIONS WITH TRANSFERS

This preprint was accepted March, 2000
Contact: K. Zainoulline

ABSTRACT:
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.


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