K-groups for rings of finite Cohen–Macaulay type
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Henrik Holm
Abstract
For a local Cohen–Macaulay ring R of finite CM-type, Yoshino has applied methods of Auslander and Reiten to compute the Grothendieck group K0 of the category mod R of finitely generated R-modules. For the same type of rings, we compute in this paper the first Quillen K-group K1(mod R). We also describe the group homomorphism R* → K1(mod R) induced by the inclusion functor proj R → mod R and illustrate our results with concrete examples.
It is a pleasure to thank Peter Jørgensen without whom this paper could not have been written. However, Peter did not wish to be a coauthor of this manuscript. We are also grateful to Marcel Bökstedt and Charles A. Weibel for valuable input on the Gersten–Sherman transformation, and to Christian U. Jensen for pointing out Proposition 10.3. Finally, we thank Viraj Navkal and the anonymous referee for their thoughtful comments and for making us aware of the paper [`K'-theory of a local ring of finite Cohen–Macaulay type', preprint (2012)].
© 2015 by De Gruyter
Articles in the same Issue
- Frontmatter
- Notes on occupation time fluctuations of binary branching particle systems
- On the sum of two integral squares in certain quadratic fields
- A Cesàro average of Goldbach numbers
- Groups described by element numbers
- The second main theorem for entire curves into Hilbert modular surfaces
- L∞ norms of holomorphic modular forms in the case of compact quotient
- SU(2)-Donaldson invariants of the complex projective plane
- Pairs of diagonal quadratic forms and linear correlations among sums of two squares
- The subelliptic heat kernel on the three-dimensional solvable Lie groups
- Lp boundedness of the commutators of Marcinkiewicz integrals with rough kernels
- Circle-valued Morse theory for complex hyperplane arrangements
- Atomic Hp spaces and their duals on open subsets of ℝd
- Locally contractible coset spaces
- L2 and Hp boundedness of strongly singular operators and oscillating operators on Heisenberg groups
- Finite time blow-up for semilinear wave equations with variable coefficients
- Intertwining operators of irreducible representations for exponential solvable Lie groups
- Artin's conjecture and systems of diagonal equations
- The homology of simplicial complements and the cohomology of polyhedral products
- Multivariate spectral multipliers for the Dunkl transform and the Dunkl harmonic oscillator
- Multilinear generalized Radon transforms and point configurations
- On ratios of Petersson norms for Yoshida lifts
- K-groups for rings of finite Cohen–Macaulay type
- Character degree sums of finite groups
- Tame Fréchet submanifolds of co-Banach type
- Weighted norm inequalities for Schrödinger type operators
Articles in the same Issue
- Frontmatter
- Notes on occupation time fluctuations of binary branching particle systems
- On the sum of two integral squares in certain quadratic fields
- A Cesàro average of Goldbach numbers
- Groups described by element numbers
- The second main theorem for entire curves into Hilbert modular surfaces
- L∞ norms of holomorphic modular forms in the case of compact quotient
- SU(2)-Donaldson invariants of the complex projective plane
- Pairs of diagonal quadratic forms and linear correlations among sums of two squares
- The subelliptic heat kernel on the three-dimensional solvable Lie groups
- Lp boundedness of the commutators of Marcinkiewicz integrals with rough kernels
- Circle-valued Morse theory for complex hyperplane arrangements
- Atomic Hp spaces and their duals on open subsets of ℝd
- Locally contractible coset spaces
- L2 and Hp boundedness of strongly singular operators and oscillating operators on Heisenberg groups
- Finite time blow-up for semilinear wave equations with variable coefficients
- Intertwining operators of irreducible representations for exponential solvable Lie groups
- Artin's conjecture and systems of diagonal equations
- The homology of simplicial complements and the cohomology of polyhedral products
- Multivariate spectral multipliers for the Dunkl transform and the Dunkl harmonic oscillator
- Multilinear generalized Radon transforms and point configurations
- On ratios of Petersson norms for Yoshida lifts
- K-groups for rings of finite Cohen–Macaulay type
- Character degree sums of finite groups
- Tame Fréchet submanifolds of co-Banach type
- Weighted norm inequalities for Schrödinger type operators
