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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳榮凱(Jung-kai Chen) | |
| dc.contributor.author | Hou-Yi Chen | en |
| dc.contributor.author | 陳厚伊 | zh_TW |
| dc.date.accessioned | 2021-05-20T20:01:37Z | - |
| dc.date.available | 2009-12-29 | |
| dc.date.available | 2021-05-20T20:01:37Z | - |
| dc.date.copyright | 2009-12-29 | |
| dc.date.issued | 2009 | |
| dc.date.submitted | 2009-11-04 | |
| dc.identifier.citation | 1. A. D'Agnolo and P. Polesello, Deformation quantization of
complex involutive submanifolds, in: Noncommutative geom- etry and physics, World Sci. Publ., Hackensack, NJ p. 127- 137 (2005). 2. P. Berthelot and L. Illusie, Grothendieck, A. Th eorie des in-tersections et th eor eme de Riemann-Roch. Lect. Notes Math 225. Springer, Berlin Heidelberg New York (1971). 3. R. Bezrukavnikov and D. Kaledin, Fedosov quantization in algebraic context, Mosc. Math. J. 4 p. 559-592, (2004). 4. L. Breen, On the Classi cation of 2-gerbes and 2-stacks, Ast erisque-Soc. Math. France 225 (1994). 5. A. Caldararu, Derived categories of twisted sheaves on Calabi-Yau manifolds, Ph.D thesis, Cornell University (2000). 6. Hou-Yi Chen, GAGA for DQ-algebroids, To appear in Rendiconti del Seminario Matematico dell'Universita' di Padova. 7. J. Giraud, Cohomologie non ab elienne, Grundlehren der Math. Wiss 179 Springer-Verlag (1971). 8. A. Grothendieck, SGA 1 Rev^etements etales et Groupe Fon-damental, Lecture Notes in Math. 224, Springer-Verlag, Heidelberg (1971). 9. D. Huybrechts, Fourier-Mukai transforms in algebraic vari-ety, Oxford mathematical Monographs, Oxford, (2006). 10. R. Hotta, Kiyoshi. Takeuchi, Toshiyuki Tanisaki, D- modules, Perverse sheaves, and Representation theory, Progress in Mathematics, Vol. 236, Birkhauser Boston, Cambridge, MA, 2008. 11. M. Kashiwara, D-modules and Microlocal Calculus, Iwanami series in Modern Mathematics, Iwanami Shorten, Tokyo, 2000 (in Japanese); Translations of Mathematical Monographs, Vol. 217, American Mathematical Society, Providence, RI, 2003 (in English; translated by Mutsumi Saito.) 12. ____, Quantization of contact manifolds, Publ. RIMS, Kyoto Univ. 32 p. 1-5 (1996). 13. M. Kashiwara and P. Schapira, Deformation quantization modules, To appear. 14. ____, Categories and sheaves, Grundlehren der Math. Wiss. 332, Springer-Verlag (2006). 15. M. Kontsevich, Deformation quantization of algebraic varieties, Euro-Conf erence Mosh e Flato, Part III (Dijon, 2000) Lett. Math. Phys. 56 (3) p. 271-294 (2001). 16. G. Laumon, Sur la cat egorie d eriv ee des D-modules ltr es, Algebraic geometry (M. Raumaid amd T. Shioda eds) Lecture Notes in Math. Springer-Verlag 1016 pp. 151-237 (1983). 17. P. Polesello and P. Schapira, Stacks of quantization- deformation modules over complex symplectic manifolds, Int. Math. Res. Notices 49 p. 2637-2664 (2004). 18. P. Schapira, From D-modules to deformation quantization modules, course note given at Buenos Aires, July 2008. http://www.math.jussieu.fr/ schapira/. 19. J-P. Serre, G eom etrie alg ebrique et g eom etrie analytique, Ann. Inst. Fourier 6 (1956), 1-42. 20. A. Yekutieli, Deformation quantization in algebraic geometry, Adv. Math. 198 pp. 383-432 (2005). | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/8802 | - |
| dc.description.abstract | The theory of deformation quantization modules have a great
improvement recently. In this thesis, we prove two basic theorems about this theory. The first theorem is a generalization of Riemann-Roch theorem for D-modules. We generalize the (algebraic) Riemann-Roch theorem for D-modules of [16] to (analytic) W -modules. The second theorem is a generalization of Serre's GAGA theorem [see 6]. Let X be a smooth complex projective variety with associated compact complex manifold X_{an}. If A_{X} is a DQ-algebroid on X, then there is an induced DQ-algebroid on X_{an}. We show that the natural functor from the derived category of bounded complexes of A_{X}-modules with coherent cohomologies to the derived category of bounded complexes of A_{X_{an}}-modules with coherent cohomologies is an equivalence. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-20T20:01:37Z (GMT). No. of bitstreams: 1 ntu-98-D93221002-1.pdf: 2613750 bytes, checksum: 1d9e4fab832b70560bcc3a27de448421 (MD5) Previous issue date: 2009 | en |
| dc.description.tableofcontents | Introduction......1
1. Preliminary......4 2. Review on the GAGA theorem.....12 3. Review on the results of Laumon......17 4. The rst main theorem......21 5. Applications to D-modules......30 6. Review on DQ-modules (after K-S)......33 7. Analytization of a DQ-algebroid......42 8. The second main theorem......44 Reference......53 | |
| dc.language.iso | en | |
| dc.title | 量子形變模上的兩個定理 | zh_TW |
| dc.title | Two theorems for deformation quantization modules | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 98-1 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 王金龍(Chin-Lung Wang),林惠雯(Hui-Wen Lin),程舜仁(Cheng, Shun-Jen),江謝宏任(Hung-Jen Chiang-Hsieh) | |
| dc.subject.keyword | 量子形變模, | zh_TW |
| dc.subject.keyword | deformation quantization modules, | en |
| dc.relation.page | 55 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2009-11-04 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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