# 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} }

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…

## 98 Citations

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