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DIMENSIONS OF TRIANGULATED CATEGORIES VIA KOSZUL OBJECTS
"... Abstract. Lower bounds for the dimension of a triangulated category are provided. These bounds are applied to stable derived categories of Artin algebras and of commutative complete intersection local rings. As a consequence, one obtains bounds for the representation dimensions of certain Artin alge ..."
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Cited by 20 (10 self)
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Abstract. Lower bounds for the dimension of a triangulated category are provided. These bounds are applied to stable derived categories of Artin algebras and of commutative complete intersection local rings. As a consequence, one obtains bounds for the representation dimensions of certain Artin
Complete Intersections in Regular Local Rings ∗
"... Let R be a 3dimensional regular local ring. Let p be a dimension one prime of R. We are concerned with two problems: (1) when is p a complete intersection and (2) when is p a set theoretic complete intersection? We prove a result of Cowsik and Nori to answer (1) and several results answering (2). C ..."
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Let R be a 3dimensional regular local ring. Let p be a dimension one prime of R. We are concerned with two problems: (1) when is p a complete intersection and (2) when is p a set theoretic complete intersection? We prove a result of Cowsik and Nori to answer (1) and several results answering (2
Complete intersection dimension
"... A new homological invariant is introduced for a finite module over a commutative noetherian ring: its CIdimension. In the local case, sharp quantitative and structural data are obtained for modules of finite CIdimension, providing the first class of modules of (possibly) ..."
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Cited by 65 (11 self)
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A new homological invariant is introduced for a finite module over a commutative noetherian ring: its CIdimension. In the local case, sharp quantitative and structural data are obtained for modules of finite CIdimension, providing the first class of modules of (possibly)
Locally complete intersection
"... homomorphisms and a conjecture of Quillen on the vanishing of cotangent homology ..."
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homomorphisms and a conjecture of Quillen on the vanishing of cotangent homology
COMPLETE INTERSECTIONS AND DERIVED CATEGORIES
, 2009
"... We propose a definition of when a triangulated category should be considered a complete intersection. We show that for the derived category of a complete local Noetherian commutative ring R, the condition on the derived category D(R) holds precisely when R is a complete intersection in the classica ..."
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We propose a definition of when a triangulated category should be considered a complete intersection. We show that for the derived category of a complete local Noetherian commutative ring R, the condition on the derived category D(R) holds precisely when R is a complete intersection
Frobenius Powers Of Complete Intersections
, 2000
"... Introduction Let R be a commutative noetherian local ring of characteristic p > 0, and let : R ! R be the Frobenius endomorphism, (a) = a p . Each iteration r denes on R a new structure of Rmodule, denoted r R, for which a b = a p r b. In 1969 Kunz [7, (3.3)] observed that if R ..."
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Cited by 16 (4 self)
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Introduction Let R be a commutative noetherian local ring of characteristic p > 0, and let : R ! R be the Frobenius endomorphism, (a) = a p . Each iteration r denes on R a new structure of Rmodule, denoted r R, for which a b = a p r b. In 1969 Kunz [7, (3.3)] observed that if R
Noncommutative Henselian Rings
, 2008
"... Noncommutative Henselian rings are defined and it is shown that a local ring which is complete and separated in the topology defined by its maximal ideal is Henselian provided that it is almost commutative. We define noncommutative Henselian rings and give some examples of them. Here, all rings ar ..."
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Noncommutative Henselian rings are defined and it is shown that a local ring which is complete and separated in the topology defined by its maximal ideal is Henselian provided that it is almost commutative. We define noncommutative Henselian rings and give some examples of them. Here, all rings
On The Embedding Of A Commutative Ring In A Local Ring
, 1999
"... this paper we consider conditions in order that there exists an embedding of R in a local ring. This leads naturally to an examination of conditions in order that a quasilocal ring (R; m) be dominated by a local ring. This, in turn, leads to a study of extensions of the residue field of a quasilocal ..."
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this paper we consider conditions in order that there exists an embedding of R in a local ring. This leads naturally to an examination of conditions in order that a quasilocal ring (R; m) be dominated by a local ring. This, in turn, leads to a study of extensions of the residue field of a
Results 1  10
of
740,320