A Flatness Property for Filtered $\mathcal{D}$-modules
نویسندگان
چکیده
منابع مشابه
A Flatness Property for Filtered D-modules
Let M be a coherent module over the ring DX of linear differential operators on an analytic manifold X and let Z1, · · · , Z k be k germs of transverse hypersurfaces at a point x ∈ X. The Malgrange-Kashiwara V-filtrations along these hypersurfaces, associated with a given presentation of the germ of M at x, give rise to a multifiltration U • (M) of Mx as in Sabbah's paper [9] and to an analytic...
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We prove various extensions of the Local Flatness Criterion over a Noetherian local ring R with residue field k. For instance, if Ω is a complete R-module of finite projective dimension, then Ω is flat if and only if Torn (Ω, k) = 0 for all n = 1, . . . , depth(R). In low dimensions, we have the following criteria. If R is onedimensional and reduced, then Ω is flat if and only if Tor1 (Ω, k) = ...
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For a coherent filtered D-module we show that the dual of each graded piece over the structure sheaf is isomorphic to a certain graded piece of the ring-theoretic local cohomology complex of the graded quotient of the dual of the filtered D-module along the zero-section of the cotangent bundle. This follows from a similar assertion for coherent graded modules over a polynomial algebra over the ...
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ژورنال
عنوان ژورنال: Publications of the Research Institute for Mathematical Sciences
سال: 2007
ISSN: 0034-5318
DOI: 10.2977/prims/1199403810