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The relative form of Gersten's conjecture for power series over a complete discrete valuation ring


Authors: L. Reid and C. Sherman
Journal: Proc. Amer. Math. Soc. 109 (1990), 611-613
MSC: Primary 19D99; Secondary 13D15, 16E20, 18F25
MathSciNet review: 1013980
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Abstract: A relative form of Gersten's Conjecture is established for a ring of formal power series over a complete discrete valuation ring. The main corollaries are that the absolute version of Gersten's Conjecture is valid for such a ring if it is valid for arbitrary discrete valuation rings, and, consequently, that the conjecture is true for such a ring if we use $ K$-theory with finite coefficients of order prime to the characteristic of the residue field.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1013980-4
Keywords: Algebraic $ K$-theory, Gersten's conjecture
Article copyright: © Copyright 1990 American Mathematical Society