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arXiv · 1703.05915

Iterated line integrals over Laurent series fields of characteristic p

Ambrus Pál
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Abstract

Inspired by Besser's work on Coleman integration, we use $\nabla$-modules to define iterated line integrals over Laurent series fields of characteristic $p$ taking values in double cosets of unipotent $n\times n$ matrices with coefficients in the Robba ring divided out by unipotent $n\times n$ matrices with coefficients in the bounded Robba ring on the left and by unipotent $n\times n$ matrices with coefficients in the constant field on the right. We reach our definition by looking at the analogous theory for Laurent series fields of characteristic $0$ first, and reinterpreting the classical formal logarithm in terms of $\nabla$-modules on formal schemes. To illustrate that the new $p$-adic theory is non-trivial, we show that it includes the $p$-adic formal logarithm as a special case.

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Ambrus Pál. 2017-03-17. Iterated line integrals over Laurent series fields of characteristic p. https://arxiv.org/abs/1703.05915

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