Good formal structures for flat meromorphic connections, II: Excellent schemes
Given a flat meromorphic connection on an excellent scheme over a field of characteristic zero, we prove existence of good formal structures after blowing up; this extends a theorem of Mochizuki for algebraic varieties. The argument combines a numerical criterion for good formal structures from a pr...
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| Format: | Article |
| Language: | en_US |
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American Mathematical Society
2011
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| Online Access: | http://hdl.handle.net/1721.1/63121 |
| _version_ | 1811077492634550272 |
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| author | Kedlaya, Kiran S. |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Kedlaya, Kiran S. |
| author_sort | Kedlaya, Kiran S. |
| collection | MIT |
| description | Given a flat meromorphic connection on an excellent scheme over a field of characteristic zero, we prove existence of good formal structures after blowing up; this extends a theorem of Mochizuki for algebraic varieties. The argument combines a numerical criterion for good formal structures from a previous paper, with an analysis based on the geometry of an associated valuation space (Riemann-Zariski space). We obtain a similar result over the formal completion of an excellent scheme along a closed subscheme. If we replace the excellent scheme by a complex analytic variety, we obtain a similar but weaker result in which the blowup can only be constructed in a suitably small neighborhood of a prescribed point. |
| first_indexed | 2024-09-23T10:43:53Z |
| format | Article |
| id | mit-1721.1/63121 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T10:43:53Z |
| publishDate | 2011 |
| publisher | American Mathematical Society |
| record_format | dspace |
| spelling | mit-1721.1/631212022-09-30T22:35:34Z Good formal structures for flat meromorphic connections, II: Excellent schemes Good formal structures for flat meromorphic connections, II: Excellent schemes Kedlaya, Kiran S. Massachusetts Institute of Technology. Department of Mathematics Kedlaya, Kiran S. Kedlaya, Kiran S. Given a flat meromorphic connection on an excellent scheme over a field of characteristic zero, we prove existence of good formal structures after blowing up; this extends a theorem of Mochizuki for algebraic varieties. The argument combines a numerical criterion for good formal structures from a previous paper, with an analysis based on the geometry of an associated valuation space (Riemann-Zariski space). We obtain a similar result over the formal completion of an excellent scheme along a closed subscheme. If we replace the excellent scheme by a complex analytic variety, we obtain a similar but weaker result in which the blowup can only be constructed in a suitably small neighborhood of a prescribed point. National Science Foundation (U.S.) (CAREER grant DMS-0545904) United States. Defense Advanced Research Projects Agency (DARPA grant HR0011-09-1-0048) Massachusetts Institute of Technology Institute for Advanced Study 2011-05-25T20:26:41Z 2011-05-25T20:26:41Z 2010-09 2010-07 Article http://purl.org/eprint/type/JournalArticle 1088-6834 0894-0347 http://hdl.handle.net/1721.1/63121 Kedlaya, Kiran S. "Good formal structures for flat meromorphic connections, II: Excellent schemes." J. Amer. Math. Soc. 24 (2011), 183-229.© 2011, American Mathematical Society. en_US http://dx.doi.org/10.1090/S0894-0347-2010-00681-9 Journal of the American Mathematical Society Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf American Mathematical Society Prof. Kedlaya |
| spellingShingle | Kedlaya, Kiran S. Good formal structures for flat meromorphic connections, II: Excellent schemes |
| title | Good formal structures for flat meromorphic connections, II: Excellent schemes |
| title_full | Good formal structures for flat meromorphic connections, II: Excellent schemes |
| title_fullStr | Good formal structures for flat meromorphic connections, II: Excellent schemes |
| title_full_unstemmed | Good formal structures for flat meromorphic connections, II: Excellent schemes |
| title_short | Good formal structures for flat meromorphic connections, II: Excellent schemes |
| title_sort | good formal structures for flat meromorphic connections ii excellent schemes |
| url | http://hdl.handle.net/1721.1/63121 |
| work_keys_str_mv | AT kedlayakirans goodformalstructuresforflatmeromorphicconnectionsiiexcellentschemes |