# Good formal structures for flat meromorphic connections, I: Surfaces

@article{Kedlaya2008GoodFS,
title={Good formal structures for flat meromorphic connections, I: Surfaces},
author={Kiran S. Kedlaya},
journal={Duke Mathematical Journal},
year={2008},
volume={154},
pages={343-418}
}
• K. Kedlaya
• Published 2 November 2008
• Mathematics
• Duke Mathematical Journal
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…
94 Citations

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