Bounds on the Castelnuovo-Mumford regularity of tensor products

Caviglia, Giulio

doi:10.1090/s0002-9939-07-08222-6

Cited by 26 publications

(30 citation statements)

References 7 publications

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“…The following result generalizes a result of Caviglia in his thesis (see [Ca,3.10]). and our hypothesis implies that E pq 2 = 0 for p = n − q and q = i 0 , and for p + q > n. This in turn shows that E pq 2 E pq ∞ for any p and q.…”

Section: Regularity Of Ext Modulessupporting

confidence: 83%

Generalized local cohomology and regularity of Ext modules

Chardin

Divaani-Aazar

2008

Journal of Algebra

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Let R be a Noetherian standard graded ring, and M and N two finitely generated graded R-modules. We introduce reg R (M, N ) by using the notion of generalized local cohomology instead of local cohomology, in the definition of regularity. We prove that reg R (M, N ) is finite in several cases. In the case that the base ring is a field, we show thatThis formula, together with a graded version of duality for generalized local cohomology, gives a formula for the minimum of the initial degrees of some Ext modules (in the case R is Cohen-Macaulay), of which the three usual definitions of regularity are special cases. Bounds for regularity of certain Ext modules are obtained, using the same circle of ideas.

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Section: Regularity Of Ext Modulessupporting

confidence: 83%

Generalized local cohomology and regularity of Ext modules

Chardin

Divaani-Aazar

2008

Journal of Algebra

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“…The reader may also confer [Ca,Section 3] for similar proofs for the regularity of modules over a commutative ring.…”

Section: Subadditive Regularity Bounds On Schemesmentioning

confidence: 99%

Ample filters and Frobenius amplitude

Keeler¹

2010

Journal of Algebra

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Let $X$ be a projective scheme over a field. We show that the vanishing cohomology of any sequence of coherent sheaves is closely related to vanishing under pullbacks by the Frobenius morphism. We also compare various definitions of ample locally free sheaf and show that the vanishing given by the Frobenius morphism is, in a certain sense, the strongest possible. Our work can be viewed as various generalizations of the Serre Vanishing Theorem.Comment: 15 pages, major improvement in result

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“…Notably a huge number of upper bounds for the regularity have been established. We mention only a few more recent references to such results, namely [1,3,4,6,2,[9][10][11]18,20].…”

Section: What Bounds Cohomology Of a Projective Scheme?mentioning

confidence: 99%

Castelnuovo–Mumford regularity of deficiency modules

2009

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Let d ∈ N and let M be a finitely generated graded module of dimension d over a Noetherian homogeneous ring R with local Artinian base ring R 0 . Let beg(M), gendeg(M) and reg(M) respectively denote the beginning, the generating degree and the Castelnuovo-Mumford regularity of M. If i ∈ N 0 and n ∈ Z , let d i M (n) denote the R 0 -length of the n-th graded component of the i-th R + -transform module D i R+ (M) of M and let K i (M) denote the i-th deficiency module of M. Our main result says, that reg(K i (M)) is bounded in terms of beg(M) and the "diagonal values" d j M (− j) with j = 0, . . . ,d − 1. As an application of this we get a number of further bounding results for reg(K i (M)).

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Bounds on the Castelnuovo-Mumford regularity of tensor products

Cited by 26 publications

References 7 publications

Generalized local cohomology and regularity of Ext modules

Generalized local cohomology and regularity of Ext modules

Ample filters and Frobenius amplitude

Castelnuovo–Mumford regularity of deficiency modules

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