References
Transcription
References
6 NICHOLAS SWITALA References [1] Jan-Erik Björk, Rings of differential operators, North-Holland Mathematical Library 21, North-Holland Publishing, Amsterdam-New York, 1979. [2] Manuel Blickle and Raphael Bondu, ‘Local cohomology multiplicities in terms of étale cohomology’, Ann. Inst. Fourier 55 (7) (2005), 2239-2256. [3] Manuel Blickle, Bhargav Bhatt, Gennady Lyubeznik, Anurag Singh, and Wenliang Zhang, ‘Local cohomology modules of a smooth Z-algebra have finitely many associated primes’, Invent. Math. 197 (3) (2014), 509-519. [4] Markus Brodmann and Rodney Sharp, Local cohomology, second edition, Cambridge Studies in Advanced Mathematics 136, Cambridge University Press, Cambridge, 2013. [5] Arno van den Essen, Fuchsian modules, Ph.D. thesis, Katholieke universiteit Nijmegen (1979). [6] Arno van den Essen, ‘Le noyau de l’opérateur ∂x∂n agissant sur un Dn -module’, C.R. Acad. Sci. Paris 288 (1979), 687-690. [7] Arno van den Essen, ‘Un D-module holonome tel que le conoyau de l’opérateur ∂x∂n soit non-holonome’, C.R. Acad. Sci. Paris 295 (1982), 455-457. [8] Arno van den Essen, ‘Le conoyau de l’opérateur ∂x∂n agissant sur un Dn -module holonome’, C.R. Acad. Sci. Paris 296 (1983), 903-906. [9] Arno van den Essen, ‘The cokernel of the operator ∂x∂n acting on a Dn -module II’, Compos. Math. 56 (2) (1985), 259-269. [10] Ricardo Garcı́a López and Claude Sabbah, ‘Topological computation of local cohomology multiplicities’, Collect. Math. 49 (2-3) (1998), 317-324. [11] Alexander Grothendieck and Jean Dieudonné, ‘Eléments de géométrie algébrique III: Étude cohomologique des faisceaux cohérents, première partie’, Publ. Math. IHÉS 11 (1961). [12] Alexander Grothendieck and Jean Dieudonné, ‘Eléments de géométrie algébrique IV: Étude locale des schémas et des morphismes de schémas, quatrième partie’, Publ. Math. IHÉS 32 (1967). [13] Alexander Grothendieck and Michèle Raynaud, Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux (SGA 2), Documents Mathématiques 4, Société Mathématique de France, Paris, 2005. [14] Robin Hartshorne, Residues and duality, Springer Lecture Notes in Mathematics 20, Springer-Verlag, Berlin, 1966. [15] Robin Hartshorne, Local cohomology, Springer Lecture Notes in Mathematics 41, Springer-Verlag, Berlin, 1967. [16] Robin Hartshorne, ‘On the de Rham cohomology of algebraic varieties’, Publ. Math. IHÉS 45 (1975), 5-99. [17] Craig Huneke, ‘Problems on local cohomology’, 93-108, Free resolutions in commutative algebra and algebraic geometry (Sundance, 1990), Research Notes in Mathematics 2, Jones and Bartlett, Boston, 1992. [18] Craig Huneke and Rodney Sharp, ‘Bass numbers of local cohomology modules’, Trans. Amer. Math. Soc. 339 (1993), 765-779. [19] Gennady Lyubeznik, ‘Finiteness properties of local cohomology modules’, Invent. Math. 113 (1) (1993), 41-55. [20] Gennady Lyubeznik, ‘A partial survey of local cohomology’, 121-154, Local cohomology and its applications (Guanajuato, 1999), Lecture Notes in Pure and Appl. Math. 226, Dekker, New York, 2002. [21] Eben Matlis, ‘Injective modules over Noetherian rings’, Pacific J. Math. 8 (1958), 511-528. [22] Luis Núñez-Betancourt, Emily Witt, and Wenliang Zhang, ‘A survey on the Lyubeznik numbers’, arXiv preprint arXiv:1406.7590 (2014). [23] Arthur Ogus, ‘Local cohomological dimension of algebraic varieties’, Ann. of Math. 98 (1973), 1-34. [24] Tony Puthenpurakal, ‘Associated primes of local cohomology modules over regular rings’, arXiv preprint arXiv:1411.2734 (2014). [25] Anurag Singh, ‘p-torsion elements in local cohomology modules’, Math. Res. Lett. 7 (2000), 165-176. [26] Nicholas Switala, ‘Lyubeznik numbers for nonsingular projective varieties’, Bull. London Math. Soc. 47 (1) (2015), 1-6. [27] Nicholas Switala, ‘Van den Essen’s theorem on the de Rham cohomology of a holonomic D-module over a formal power series ring’ (2015), arXiv preprint arXiv:1505.01788, submitted for publication. [28] Nicholas Switala, ‘On the de Rham homology and cohomology of a complete local ring in equicharacteristic zero’, in preparation. [29] Nicholas Switala, Some local cohomology invariants of nonsingular projective varieties and complete local rings, Ph.D. thesis, University of Minnesota (2015). [30] Wenliang Zhang, ‘Lyubeznik numbers of projective schemes’, Adv. Math. 228 (2011), 575-616.