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Good formal structures for flat meromorphic connections, II: Excellent schemes


Author: Kiran S. Kedlaya
Journal: J. Amer. Math. Soc. 24 (2011), 183-229
MSC (2010): Primary 14F10; Secondary 32C38
DOI: https://doi.org/10.1090/S0894-0347-2010-00681-9
Published electronically: September 17, 2010
MathSciNet review: 2726603
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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.


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Additional Information

Kiran S. Kedlaya
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139
Email: kedlaya@mit.edu

DOI: https://doi.org/10.1090/S0894-0347-2010-00681-9
Received by editor(s): January 6, 2010
Received by editor(s) in revised form: July 14, 2010
Published electronically: September 17, 2010
Additional Notes: The author was supported by NSF CAREER grant DMS-0545904, DARPA grant HR0011-09-1-0048, MIT (NEC Fund, Green Career Development Professorship), IAS (NSF grant DMS-0635607, James D. Wolfensohn Fund).
Article copyright: © Copyright 2010 Kiran S. Kedlaya

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