Abstract
In the spirit of the section conjecture, a section should behave like a rational point. In particular, we should be able to evaluate a function in a section. At least for invertible functions this can be achieved via Kummer theory, see Definition 57, if we accept that the values will be taken in a certain completion of the multiplicative group of the ground field.
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References
Jannsen, U.: Continuous étale cohomology. Math. Annalen 280, 207–245 (1988)
Serre, J.-P.: Local Fields. Graduate Text in Mathematics, vol. 67, viii + 260 pp. Springer, New York (1979)
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Stix, J. (2013). Evaluation of Units. In: Rational Points and Arithmetic of Fundamental Groups. Lecture Notes in Mathematics, vol 2054. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30674-7_5
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DOI: https://doi.org/10.1007/978-3-642-30674-7_5
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