Differential operators on monomial rings

Traves, William N.

doi:10.1016/s0022-4049(97)00170-9

Cited by 17 publications

(23 citation statements)

References 9 publications

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“…It is easy to see that its composition with the classical Fourier transformation (30) gives the same as (29), which proves the commutativity of the above square.…”

Section: Principal Symbols and Inverse Limitsmentioning

confidence: 64%

One-dimensional infinitesimal-birational duality through differential operators

Maszczyk

2006

Fund. Math.

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Abstract. The structure of filtered algebras of Grothendieck's differential operators on a smooth fat point in a curve and graded Poisson algebras of their principal symbols is explicitly determined. A related infinitesimal-birational duality realized by a Springer type resolution of singularities and the Fourier transformation is presented. This algebrogeometrical duality is quantized in appropriate sense and its quantum origin is explained.It seems that our ship is arriving at a coast, but the land is still hidden in the fog.

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“…It is easy to see that its composition with the classical Fourier transformation (30) gives the same as (29), which proves the commutativity of the above square.…”

Section: Principal Symbols and Inverse Limitsmentioning

confidence: 64%

One-dimensional infinitesimal-birational duality through differential operators

Maszczyk

2006

Fund. Math.

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“…Theorem 5 can also be used to recover a result due to Schreiner [5] (also, see Traves [8]): Nakai's conjecture holds for Stanley-Reisner rings (that is, for subvarieties of A N k which are the union of coordinate subspaces). More generally, the theorem implies that Nakai's conjecture holds for varieties all of whose components are smooth, as remarked by Lazarsfeld.…”

Section: Theoremmentioning

confidence: 85%

Nakai’s conjecture for varieties smoothed by normalization

Traves

1999

Proc. Amer. Math. Soc.

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“…. , p n are its minimal primes, τ fg (R) = n i=1 ann p i , after which Traves [T,Theorem 5.8] gave a D-module proof of the same result.…”

Section: Proposition 74 For Any Reduced Noetherian Ring (Of Any Chamentioning

confidence: 92%

A dual to tight closure theory

Epstein¹,

Schwede

2014

Nagoya Mathematical Journal

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We introduce an operation on modules over an $F$-finite ring of characteristic $p$. We call this operation \emph{tight interior}. While it exists more generally, in some cases this operation is equivalent to the Matlis dual of tight closure. Moreover, the interior of the ring itself is simply the big test ideal. We directly prove, without appeal to tight closure, results analogous to persistence, colon capturing, and working modulo minimal primes, and we begin to develop a theory dual to phantom homology. Using our dual notion of persistence, we obtain new and interesting transformation rules for tight interior, and so in particular for the test ideal, which complement the main results of a recent paper of the second author and K. Tucker. Using our theory of phantom homology, we prove a vanishing theorem for maps of Ext. We also compare our theory to M. Blickle's notion of Cartier modules, and in the process, we prove new existence results for Blickle's test submodule. Finally, we apply the theory we developed to the study of test ideals in non-normal rings, proving that the finitistic test ideal coincides with the big test ideal in some cases.Comment: References added and other minor changes. To appear in the Nagoya Mathematical Journa

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Differential operators on monomial rings

Cited by 17 publications

References 9 publications

One-dimensional infinitesimal-birational duality through differential operators

One-dimensional infinitesimal-birational duality through differential operators

Nakai’s conjecture for varieties smoothed by normalization

A dual to tight closure theory

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