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

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

2010-01-04

arxiv.org/abs/1001.0544v2

Mathematics

Algebraic Geometry

54 pages; v2: refereed version; minor corrections

Scientific paper

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 small neighborhood of a prescribed point.

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