Algebraic flat connections and o-minimality
Algebraic Geometry
2025-07-22 v2
Abstract
We prove that an algebraic flat connection has definable flat sections in the analytic exponential structure if and only if it is regular singular with unitary monodromy eigenvalues at infinity, refining previous work of Bakker and Mullane. This provides an o minimal characterisation of classical properties of the Gauss-Manin connection. v2: a few typos removed. Appears in the Laumon Volume, Springer Verlag, Simons subseries.
Cite
@article{arxiv.2506.07498,
title = {Algebraic flat connections and o-minimality},
author = {Hélène Esnault and Moritz Kerz},
journal= {arXiv preprint arXiv:2506.07498},
year = {2025}
}
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9 pages