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

Albinism

Brauer–Manin and Descent Obstructions the local analogues of the section conjecture over real and .-adic local fields. The present Chapter concerns the usual next step, when the local problem is considered settled (which it is not for the section conjecture). In order to possibly arise from a common global rational point, the tuple of

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Paraplegia

Nilpotent Sections truncated versions of bounded nilpotency. These quotients have been studied in the realm of the section conjecture by Ellenberg around 2000, unpublished, and later by Wickelgren in her thesis (Wickelgren, Lower central series obstructions to homotopy sections of curves over number fields, Thesis, S

objection

Book 2013perbolic algebraic curve over a number field in terms of the arithmetic of its fundamental group. While the conjecture is still open today in 2012, its study has revealed interesting arithmetic for curves and opened connections, for example, to the question whether the Brauer-Manin obstruction is th

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喊叫

Basic Geometric Operations in Terms of Sectionsiour 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.

积极词汇

0075-8434 ometry: from the history of the subject to the state of the The section conjecture in anabelian geometry, announced by Grothendieck in 1983, is concerned with a description of the set of rational points of a hyperbolic algebraic curve over a number field in terms of the arithmetic of its fundamental

Endemic

Injectivity in the Section Conjecturemetrically connected variety, the injectivity of the Kummer map (after arbitrary finite scalar extension) implies that the fundamental group must be large in the sense of Kollár, see Proposition 77, which imposes strong geometric constraints on possible higher dimensional anabelian varieties.

伴随而来

The Space of Sections in the Arithmetic Case and the Section Conjecture in Coversows that, just like rational points, sections obey Galois descent, see Corollary 107. Furthermore, we examine . and . for the section conjecture with respect to a finite étale map. The discussion relies on Chap. 3.

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