Good formal structures for flat meromorphic connections, II: Excellent schemes
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good_formal_structures_for_flat_meromorphic_connections_2_unlocked.pdf
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861 KB
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Checksum (MD5)
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Author(s)
Kedlaya, Kiran S.
Alternative Title
Good formal structures for flat meromorphic connections, II: Excellent schemes
Date Issued
September 2010
Journal
Journal of the American Mathematical Society
Publisher
American Mathematical Society
Citation
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.
Version
Final published version
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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.
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DOI of Published Version
https://doi.org/10.1090/S0894-0347-2010-00681-9
