Residues and differential operators on schemes

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Residues and differential operators on schemes

Amnon Yekutieli

Source: Duke Math. J. Volume 95, Number 2 (1998), 305-341.

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Primary Subjects: 14F40

Secondary Subjects: 13N05, 14B10, 14F10

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077229699
Mathematical Reviews number (MathSciNet): MR1652013
Zentralblatt MATH identifier: 0962.14010
Digital Object Identifier: doi:10.1215/S0012-7094-98-09509-6

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References

[BaK] D. Barlet and M. Kashiwara, Le réseau $L\sp 2$ d'un système holonome régulier, Invent. Math. 86 (1986), no. 1, 35–62.

Mathematical Reviews (MathSciNet): MR88f:32038

Zentralblatt MATH: 0598.32014

Digital Object Identifier: doi:10.1007/BF01391494

[Be] A. A. Beilinson, Residues and adèles, Funktsional. Anal. i Prilozhen. 14 (1980), no. 1, 44–45, Functional Anal. Appl. 14 (1980), 34–35.

Mathematical Reviews (MathSciNet): MR81f:14010

Zentralblatt MATH: 0509.14018

[Bj] J. E. Björk, Rings of Differential Operators, North-Holland Math. Library, vol. 21, North-Holland, Amsterdam, 1979.

Mathematical Reviews (MathSciNet): MR82g:32013

Zentralblatt MATH: 0499.13009

[BlO] S. Bloch and A. Ogus, Gersten's conjecture and the homology of schemes, Ann. Sci. École Norm. Sup. (4) 7 (1974), 181–201.

Mathematical Reviews (MathSciNet): MR54:318

Zentralblatt MATH: 0307.14008

[Bo] A. Borel, P.-P. Grivel, B. Kaup, A. Haefliger, B. Malgrange, and F. Ehlers, Algebraic $D$-modules, Perspectives in Mathematics, vol. 2, Academic Press Inc., Boston, MA, 1987.

Mathematical Reviews (MathSciNet): MR89g:32014

Zentralblatt MATH: 0642.32001

[Bou] N. Bourbaki, Elements of Mathematics: Commutative Algebra, Springer-Verlag, Berlin, 1989.

Zentralblatt MATH: 0666.13001

Mathematical Reviews (MathSciNet): MR979760

[Br] J.-L. Brylinski, La classe fondamentale d'une variété algébrique engendre le ${\scr D}$-module qui calcule sa cohomologie d'intersection, Astérisque (1985), no. 130, 260–271.

Mathematical Reviews (MathSciNet): MR87j:32036

Zentralblatt MATH: 0568.14010

[BrK] J.-L. Brylinski and M. Kashiwara, Kazhdan-Lusztig conjecture and holonomic systems, Invent. Math. 64 (1981), no. 3, 387–410.

Mathematical Reviews (MathSciNet): MR83e:22020

Zentralblatt MATH: 0473.22009

Digital Object Identifier: doi:10.1007/BF01389272

[EZ] F. El Zein, Complexe dualisant et applications à la classe fondamentale d'un cycle, Bull. Soc. Math. France Mém. (1978), no. 58, 93.

Mathematical Reviews (MathSciNet): MR80h:14009

Zentralblatt MATH: 0388.14002

[Gr] A. Grothendieck, On the de Rham cohomology of algebraic varieties, Inst. Hautes Études Sci. Publ. Math. 29 (1966), 95–103.

Mathematical Reviews (MathSciNet): MR33:7343

Zentralblatt MATH: 0145.17602

[GrD]¹ A. Grothendieck and J. Dieudonné, Éléments de géométrie algébrique, I. Le langage des schémas, Inst. Hautes Études Sci. Publ. Math. 4 (1960), 228.

Mathematical Reviews (MathSciNet): MR29:1207

Zentralblatt MATH: 0118.36206

[GrD]² A. Grothendieck and J. Dieudonné, Éléments de géométrie algébrique, II. Étude globale élémentaire de quelques classes de morphismes, Inst. Hautes Études Sci. Publ. Math. 8 (1961), 222.

Mathematical Reviews (MathSciNet): MR36:177b

Zentralblatt MATH: 0118.36206

[GrD]³ A. Grothendieck and J. Dieudonné, Éléments de géométrie algébrique, III. Étude cohomologique des faisceaux cohérents. I, Inst. Hautes Études Sci. Publ. Math. 11 (1961), 167.

Mathematical Reviews (MathSciNet): MR29:1209

Zentralblatt MATH: 0118.36206

[GrD]⁴ A. Grothendieck and J. Dieudonné, Éléments de géométrie algébrique, III. Étude cohomologique des faisceaux cohérents. II, Inst. Hautes Études Sci. Publ. Math. 17 (1963), 91.

Mathematical Reviews (MathSciNet): MR29:1210

Zentralblatt MATH: 0122.16102

[GrD]⁵ A. Grothendieck and J. Dieudonné, Éléments de géométrie algébrique, IV. Étude locale des schémas et des morphismes de schémas. I, Inst. Hautes Études Sci. Publ. Math. 20 (1964), 259.

Mathematical Reviews (MathSciNet): MR30:3885

Zentralblatt MATH: 0136.15901

[GrD]⁶ A. Grothendieck and J. Dieudonné, Éléments de géométrie algébrique, IV. Étude locale des schémas et des morphismes de schémas. II, Inst. Hautes Études Sci. Publ. Math. 24 (1965), 231.

Mathematical Reviews (MathSciNet): MR33:7330

Zentralblatt MATH: 0135.39701

[GrD]⁷ A. Grothendieck and J. Dieudonné, Éléments de géométrie algébrique, IV. Étude locale des schémas et des morphismes de schémas. III, Inst. Hautes Études Sci. Publ. Math. 28 (1966), 255.

Mathematical Reviews (MathSciNet): MR36:178

Zentralblatt MATH: 0144.19904

[GrD]⁸ A. Grothendieck and J. Dieudonné, Éléments de géométrie algébrique, IV. Étude locale des schémas et des morphismes de schémas IV, Inst. Hautes Études Sci. Publ. Math. 32 (1967), 361.

Mathematical Reviews (MathSciNet): MR39:220

Zentralblatt MATH: 0153.22301

[Ha1] R. Hartshorne, Residues and Duality, Lecture Notes in Math., vol. 20, Springer-Verlag, Berlin, 1966.

Mathematical Reviews (MathSciNet): MR36:5145

Zentralblatt MATH: 0212.26101

[Ha2] R. Hartshorne, On the de Rham cohomology of algebraic varieties, Inst. Hautes Études Sci. Publ. Math. (1975), no. 45, 5–99.

Mathematical Reviews (MathSciNet): MR55:5633

Zentralblatt MATH: 0326.14004

[Ho] M. P. Holland, Duality and $\mathcal{D}$-modules on curves, Bull. Soc. Math. Belg. Sér. A 43 (1991), no. 1-2, 43–48.

Mathematical Reviews (MathSciNet): MR95k:14030

Zentralblatt MATH: 0760.14007

[HoSt] M. P. Holland and J. T. Stafford, Differential operators on rational projective curves, J. Algebra 147 (1992), no. 1, 176–244.

Mathematical Reviews (MathSciNet): MR93d:16029

Zentralblatt MATH: 0753.14014

Digital Object Identifier: doi:10.1016/0021-8693(92)90259-O

[Hg] I. C. Huang, Functorial construction of Cousin complexes, preprint.

[Hu] R. Hübl, Residues of regular and meromorphic differential forms, Math. Ann. 300 (1994), no. 4, 605–628.

Mathematical Reviews (MathSciNet): MR96e:14017

Zentralblatt MATH: 0814.14022

Digital Object Identifier: doi:10.1007/BF01450504

[HK1] R. Hübl and E. Kunz, Integration of differential forms on schemes, J. Reine Angew. Math. 410 (1990), 53–83.

Mathematical Reviews (MathSciNet): MR92a:14014

Zentralblatt MATH: 0712.14006

[HK2] R. Hübl and E. Kunz, Regular differential forms and duality for projective morphisms, J. Reine Angew. Math. 410 (1990), 84–108.

Mathematical Reviews (MathSciNet): MR92a:14015

Zentralblatt MATH: 0709.14014

[HS] R. Hübl and P. Sastry, Regular differential forms and relative duality, Amer. J. Math. 115 (1993), no. 4, 749–787.

Mathematical Reviews (MathSciNet): MR94i:14022

Zentralblatt MATH: 0796.14012

[HY1] R. Hübl and A. Yekutieli, Adèles and differential forms, J. Reine Angew. Math. 471 (1996), 1–22.

Mathematical Reviews (MathSciNet): MR97d:14026

Zentralblatt MATH: 0847.14006

[HY2] R. Hübl and A. Yekutieli, Adelic Chern forms and application, preprint.

[Kz] N. Katz, Nilpotent connections and the monodromy theorem: Applications of a result of Turrittin, Inst. Hautes Études Sci. Publ. Math. (1970), no. 39, 175–232.

Mathematical Reviews (MathSciNet): MR45:271

Zentralblatt MATH: 0221.14007

[Kl] S. L. Kleiman, Relative duality for quasicoherent sheaves, Compositio Math. 41 (1980), no. 1, 39–60.

Mathematical Reviews (MathSciNet): MR81m:14017

Zentralblatt MATH: 0403.14003

[Ko] G. Köthe, Topological Vector Spaces, I, Grundlehren Math. Wiss., vol. 159, Springer-Verlag, New York, 1969.

Mathematical Reviews (MathSciNet): MR40:1750

Zentralblatt MATH: 0179.17001

[KW] E. Kunz and R. Waldi, Regular Differential Forms, Contemp. Math., vol. 79, Amer. Math. Soc., Providence, 1988.

Mathematical Reviews (MathSciNet): MR90a:14021

Zentralblatt MATH: 0658.13019

[Li] J. Lipman, Dualizing Sheaves, Differentials and Residues on Algebraic Varieties, Astérisque 117 (1984), ii+138, Soc. Math. France, Montrouge.

Mathematical Reviews (MathSciNet): MR86g:14008

Zentralblatt MATH: 0562.14003

[LS] J. Lipman and P. Sastry, Regular differentials and equidimensional scheme-maps, J. Algebraic Geom. 1 (1992), no. 1, 101–130.

Mathematical Reviews (MathSciNet): MR92k:14019

Zentralblatt MATH: 0812.14011

[ML] S. Mac Lane, Homology, Classics Math., Springer-Verlag, Berlin, 1995, reprint of the 1975 ed.

Mathematical Reviews (MathSciNet): MR96d:18001

Zentralblatt MATH: 0818.18001

[MR] J. C. McConnell and J. C. Robson, Noncommutative Noetherian Rings, Pure Appl. Math., Wiley, Chichester, 1987.

Mathematical Reviews (MathSciNet): MR89j:16023

Zentralblatt MATH: 0644.16008

[Mi] J. S. Milne, Étale Cohomology, Princeton Math. Ser., vol. 33, Princeton Univ. Press, Princeton, N.J., 1980.

Mathematical Reviews (MathSciNet): MR81j:14002

Zentralblatt MATH: 0433.14012

[Sai] M. Saito, Modules de Hodge polarisables, Publ. Res. Inst. Math. Sci. 24 (1988), no. 6, 849–995.

Mathematical Reviews (MathSciNet): MR90k:32038

Zentralblatt MATH: 0691.14007

[Sa] P. Sastry, Residues and duality for algebraic schemes, Compositio Math. 101 (1996), no. 2, 133–178.

Mathematical Reviews (MathSciNet): MR98a:14029

Zentralblatt MATH: 0902.14012

[SY] P. Sastry and A. Yekutieli, On residue complexes, dualizing sheaves and local cohomology modules, Israel J. Math. 90 (1995), no. 1-3, 325–348.

Mathematical Reviews (MathSciNet): MR96f:14021

Zentralblatt MATH: 0834.14003

[Sm] S. P. Smith, The simple $\mathcal{D}$-module associated to the intersection homology complex for a class of plane curves, J. Pure Appl. Algebra 50 (1988), no. 3, 287–294.

Mathematical Reviews (MathSciNet): MR89d:14031

Zentralblatt MATH: 0654.14009

Digital Object Identifier: doi:10.1016/0022-4049(88)90106-5

[Vi] K. Vilonen, Intersection homology $\mathcal{D}$-module on local complete intersections with isolated singularities, Invent. Math. 81 (1985), no. 1, 107–114.

Mathematical Reviews (MathSciNet): MR87f:32023

Zentralblatt MATH: 0578.14018

Digital Object Identifier: doi:10.1007/BF01388774

[Ye1] A. Yekutieli, An Explicit Construction of the Grothendieck Residue Complex, Astérisque 208 (1992), 127, with an appendix by P. Sastry, Soc. Math. France, Montrouge.

Mathematical Reviews (MathSciNet): MR94e:14026

Zentralblatt MATH: 0788.14011

[Ye2] A. Yekutieli, Traces and differential operators over Beilinson completion algebras, Compositio Math. 99 (1995), no. 1, 59–97.

Mathematical Reviews (MathSciNet): MR96g:14014

Zentralblatt MATH: 0856.13019

[Ye3] A. Yekutieli, Smooth formal embeddings and the residue complex, to appear in Canad. J. Math.

Mathematical Reviews (MathSciNet): MR1638635

[Ye4] A. Yekutieli, The action of adèles on the residue complex, preprint.

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Residues and differential operators on schemes

References

Duke Mathematical Journal