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 -theory with finite coefficients of order prime to the characteristic of the residue field.

**[B]**N. Bourbaki,*Commutative algebra*, Addison-Wesley, Reading, MA, 1972.**[G]**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**, 10.1016/0021-8693(86)90193-6**[GL]**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**, 10.1016/0022-4049(87)90043-0**[Q]**D. Quillen,*Higher algebraic**-theory*, I, Lecture Notes in Math., vol. 341, Springer, Berlin and New York, 1972.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1990-1013980-4

Keywords:
Algebraic -theory,
Gersten's conjecture

Article copyright:
© Copyright 1990
American Mathematical Society