Abstract
Geometric structures that apply to rational points can sometimes be formulated in terms of sections: functorial properties of the space of sections, abelianization and base change. In favorable circumstances we establish Galois descent for sections, see Proposition 28. We furthermore study the behaviour of sections under fibrations and finite étale covers between varieties. The notion of the anabelian fibre above a section is introduced.The results of J. Stix (Math. J. Okayama Univ. 52:29–43, 2010) on the behaviour of the space of sections under Weil restriction of scalars are summarized in Sect. 3.5.
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Stix, J. (2013). Basic Geometric Operations in Terms of Sections. 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_3
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DOI: https://doi.org/10.1007/978-3-642-30674-7_3
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