The relative form of Gersten’s conjecture for power series over a complete discrete valuation ring
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- by L. Reid and C. Sherman PDF
- Proc. Amer. Math. Soc. 109 (1990), 611-613 Request permission
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.References
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N. Bourbaki, Commutative algebra, Addison-Wesley, Reading, MA, 1972.
- Henri Gillet, Gersten’s conjecture for the $K$-theory with torsion coefficients of a discrete valuation ring, J. Algebra 103 (1986), no. 1, 377–380. MR 860713, DOI 10.1016/0021-8693(86)90193-6
- Henri Gillet and Marc Levine, The relative form of Gersten’s conjecture over a discrete valuation ring: the smooth case, J. Pure Appl. Algebra 46 (1987), no. 1, 59–71. MR 894392, DOI 10.1016/0022-4049(87)90043-0 D. Quillen, Higher algebraic $K$-theory, I, Lecture Notes in Math., vol. 341, Springer, Berlin and New York, 1972.
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 109 (1990), 611-613
- MSC: Primary 19D99; Secondary 13D15, 16E20, 18F25
- DOI: https://doi.org/10.1090/S0002-9939-1990-1013980-4
- MathSciNet review: 1013980