2010/01/04 by Kiran S. Kedlaya, Kedlaya, Kiran S. · 2 citations
Mathematics · #14F10 #32C38 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Complex Variables (math.CV) #FOS: Mathematics #Meromorphic and Entire Functions #math.AG #math.CV #msc:14F10 #msc:32C38
paper · pdf · doi:10.48550/arxiv.1001.0544
54 pages; v2: refereed version; minor corrections
openalex publication_date 2010/01/04 · arxiv created 2010/07/30 · arxiv updated 2010/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.