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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 余正道(Jeng-Daw Yu) | |
| dc.contributor.author | Yi-Heng Tsai | en |
| dc.contributor.author | 蔡以恆 | zh_TW |
| dc.date.accessioned | 2022-11-23T09:16:07Z | - |
| dc.date.available | 2022-02-21 | |
| dc.date.available | 2022-11-23T09:16:07Z | - |
| dc.date.copyright | 2022-02-21 | |
| dc.date.issued | 2022 | |
| dc.date.submitted | 2022-01-31 | |
| dc.identifier.citation | 1. A. Castaño Domínguez, T. Reichelt and C. Sevenheck, Examples of hypergeometric twistor D-modules. 2019, arXiv:1803.04886. 2. A. Castaño Domínguez and C. Sevenheck, Irregular Hodge filtration of some confluent hypergeometric systems. 2019, arXiv:1707.03259v2. 3. M. Dettweiler and C. Sabbah, Hodge theory of the middle convolution. Publ. Res. Inst. Math. Sci. 49 (2013), no. 4, 761–800. 4. H. Esnault, C. Sabbah and J.-D. Yu, E1-degeneration of the irregular Hodge filtration. With an appendix by Morihiko Saito. J. Reine Angew. Math. 729 (2017), 171–227. 5. R. Fedorov, Variations of Hodge structures for hypergeometric differential operators and parabolic Higgs bundles. Int. Math. Res. Not. IMRN 2018, no. 18, 5583–5608. 6. N. M. Katz, Exponential sums and differential equations. Annals of Mathematics Studies, 124. Princeton University Press, Princeton, NJ, 1990. 7. T. Mochizuki, A twistor approach to the Kontsevich complexes. Manuscripta Math. 157 (2018), no. 1-2, 193–231. 8. Ph. Maisonobe and C. Sabbah, Aspects of the theory of D-modules, Kaiserslautern Lecture Notes (2002). 9. C. Sabbah, Irregular Hodge theory. Mém. Soc. Math. Fr. 156 (2018), vi+126 pp. 10. C. Sabbah and J.-D. Yu, On the irregular Hodge filtration of exponentially twisted mixed Hodge modules. Forum Math. Sigma 3 (2015), e9, 71 pp. 11. C. Sabbah and J.-D. Yu, Irregular Hodge numbers of confluent hypergeometric differential equations. 2019, arXiv:1812.00755v3. 12. J.-D. Yu, Irregular Hodge filtration on twisted de Rham cohomology. Manuscripta Math. 144 (2014), no. 1-2, 99–133 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/79905 | - |
| dc.description.abstract | 本文介紹了V-濾鏈並計算出指數扭曲么正秩一 D 模上的不規則Hodge濾鏈，接著，我們證明de Rham複形的不規則Hodge濾鏈和de Rham複形的延伸對數濾鏈是擬同構。對於緊支撐的de Rham上同调，我們也可以得到類似的結論。 | zh_TW |
| dc.description.provenance | Made available in DSpace on 2022-11-23T09:16:07Z (GMT). No. of bitstreams: 1 U0001-2701202211182700.pdf: 1239504 bytes, checksum: dd88f252c5453b333db418d9b005b0a1 (MD5) Previous issue date: 2022 | en |
| dc.description.tableofcontents | 口試委員審定書 i 致謝 ii 摘要 iii Abstract iv 1. Introduction 1 2. The V-filtration 4 2.1 The definitions and basic properties 4 2.2 The V-filtrations on DX-modules via Mochizuki’s approach 6 3. The V-filtrations on an Exponentially Twisted Unitary D-module of Rank 1 8 3.1 The V-filtration for z = 1 8 3.2 The V-filtration on the corresponding Rees module 11 4. The Irregular Hodge Filtrations 14 4.1 The irregular Hodge filtration on M∗ ⊗ E^f 14 4.2 The de Rham cohomology with compact support 21 5. Appendix 24 5.1 The weak V-filtrations 24 5.2 The Bernstein-Sato polynomials and specializability 25 | |
| dc.language.iso | en | |
| dc.subject | 混合Hodge模 | zh_TW |
| dc.subject | de Rham上同调 | zh_TW |
| dc.subject | 不規則Hodge濾鏈 | zh_TW |
| dc.subject | V-濾鏈 | zh_TW |
| dc.subject | D模 | zh_TW |
| dc.subject | D-module | en |
| dc.subject | de Rham cohomology | en |
| dc.subject | V-filtration | en |
| dc.subject | irregular Hodge filtration | en |
| dc.subject | mixed Hodge module | en |
| dc.title | 指數扭曲么正秩一 D 模上的不規則霍奇濾鏈 | zh_TW |
| dc.title | The Irregular Hodge Filtration on an Exponentially Twisted Unitary D-module of Rank One | en |
| dc.date.schoolyear | 110-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 王金龍(Sui-Yuan Chang),莊武諺(Yen-Wen Lu) | |
| dc.subject.keyword | D模,不規則Hodge濾鏈,V-濾鏈,de Rham上同调,混合Hodge模, | zh_TW |
| dc.subject.keyword | D-module,irregular Hodge filtration,V-filtration,de Rham cohomology,mixed Hodge module, | en |
| dc.relation.page | 29 | |
| dc.identifier.doi | 10.6342/NTU202200227 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2022-02-03 | |
| 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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