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15 August 2010 Good formal structures for flat meromorphic connections, I: Surfaces
Kiran S. Kedlaya
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Duke Math. J. 154(2): 343-418 (15 August 2010). DOI: 10.1215/00127094-2010-041

Abstract

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.

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Kiran S. Kedlaya. "Good formal structures for flat meromorphic connections, I: Surfaces." Duke Math. J. 154 (2) 343 - 418, 15 August 2010. https://doi.org/10.1215/00127094-2010-041

Information

Published: 15 August 2010
First available in Project Euclid: 16 August 2010

zbMATH: 1204.14010
MathSciNet: MR2682186
Digital Object Identifier: 10.1215/00127094-2010-041

Subjects:
Primary: 14F10
Secondary: 32C38, 32P05

Rights: Copyright © 2010 Duke University Press

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Vol.154 • No. 2 • 15 August 2010
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