Good formal structures for flat meromorphic connections, I: Surfaces
By Kiran S. Kedlaya. 2008
108 citations recorded by the source corpus.
We give a criterion under which one can obtain a good decomposition (in the sense of Malgrange) of a formal flat connection on a complex analytic or algebraic variety of arbitrary dimension. The criterion is stated in terms of the spectral behavior of differential operators, and generalizes Robba's construction of the Hukuhara-Levelt-Turrittin decomposition in the one-dimensional case. As an application, we prove the existence of good formal structures for flat meromorphic connections on surfaces after suitable blowing up; this verifies a conjecture of Sabbah, and extends a result of Mochizuki for algebraic connections. Our proof uses a finiteness argument on the valuative tree associated to a point on a surface, in order to verify the numerical criterion.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/320420e6c6bf1c804c8932f52e2e6ff6e79edcb3
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In Applied Mathematics
In Geometry and Topology
- C. Sabbah
- Kiran S. Kedlaya
- Ruochuan Liu
- Peter Scholze
- Alan G. B. Lauder
- T. Mochizuki
- Jonathan Pottharst
- Tomoyuki Abe
Citations in the corpus
- Introduction to Stokes Structures (2009, background): “Kedlaya [38] (when dimX = 2, one refers to [37]; in the algebraic setting and dimX = 2, one can use [60], and [65] for dimX > 3, see Remark 11.”
- Good formal structures for flat meromorphic connections, II: Excellent schemes (2010, methodology): “It simplifies matters greatly that the numerical criterion for good formal structures established in the first part of [26] is not limited to surfaces, but rather applies in any dimension.”