Good formal structures for flat meromorphic connections, II: Excellent schemes
Author(s)
Kedlaya, Kiran S.![Thumbnail](/bitstream/handle/1721.1/63121/good_formal_structures_for_flat_meromorphic_connections_2_unlocked.pdf.jpg?sequence=9&isAllowed=y)
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Good formal structures for flat meromorphic connections, II: Excellent schemes
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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.
Date issued
2010-09Department
Massachusetts Institute of Technology. Department of MathematicsJournal
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
ISSN
1088-6834
0894-0347