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Titlebook: Rational Points and Arithmetic of Fundamental Groups; Evidence for the Sec Jakob Stix Book 2013 Springer-Verlag Berlin Heidelberg 2013 14H3

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Basic Geometric Operations in Terms of Sectionsbelianization 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 resul
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The Space of Sections as a Topological Spacediscrete topological space, see Lemma 44, which allows important limit arguments in arithmetically relevant cases, see Lemma 48. The fundamental notion of a neighbourhood of a section is introduced and used to describe the decomposition tower of a section.
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Evaluation of Unitsection. 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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Cycle Classes in Anabelian Geometry90), Mochizuki (Invent. Math. 138(2):319–423, 1999; Mathematical Sciences Research Institute Publications, vol. 41, 2003; J. Math. Kyoto Univ. 47(3):451–539, 2007), Esnault and Wittenberg ( Mosc. Math. J. 9(3):451–467, 2009). After recalling and comparing several known constructions we describe yet
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Injectivity in the Section Conjecturetivity. The abelian approach relies on the determination of the Kummer map for abelian varieties and their arithmetic, see Corollary 71, and also on the computation of the maximal abelian quotient extension ., see Proposition 69, which for later use in Sect. 13.5 we carefully revise also for smooth
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