A New Exact Sequence for K2 and Some Consequences for Rings of Integers
نویسنده
چکیده
where t is induced by the tame symbols on R. They have also asked whether this sequence remains exact with "0 -•" inserted on the left when R is a ring of algebraic integers. In this note we announce an affirmative response when R is a discrete valuation ring, and a proof that the resulting sequence is split exact under certain additional hypotheses on R. In addition, we derive consequences of these results for a ring, O, of integers in a number field. Among these are (1) a complete determination of the groups K2(C/a) for any ideal a of O; and (2) examples of rings of integers O for which K2(0) is not generated by symbols and K2(2,O) -• K2(3,0) is not surjective. Detailed proofs will appear elsewhere.
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