Rational Points and Arithmetic of Fundamental Groups : Evidence for the Section Conjecture
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 group. While the conjecture is still open today in 2012, it...
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| Format: | Livre numérique |
| Langue: | Anglais |
| Publié: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Édition: | 1st ed. 2013. |
| Collection: | Lecture Notes in Mathematics
2054 |
| Sujets: | |
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| Note: |
L'impression du document génère 257 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Rational points and arithmetic of fundamental groups, evidence for the section conjecture, Jakob Stix, Berlin, Springer, 2013, 1 vol. (XX-249 p.), Lecture notes in mathematics, 978-3-642-30673-0 • Rational points and arithmetic of fundamental groups, evidence for the section conjecture, Jakob Stix, Berlin, Springer, 2013, 1 vol. (XX-249 p.), Lecture notes in mathematics, 978-3-642-30673-0 • Rational Points and Arithmetic of Fundamental Groups, Texte imprimé, 9783642306754 |
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| 100 | 1 | |a Stix, Jakob, |d 1974-...., |c mathématicien. | |
| 245 | 1 | 0 | |a Rational Points and Arithmetic of Fundamental Groups : |b Evidence for the Section Conjecture |c Jakob Stix. |
| 250 | |a 1st ed. 2013. | ||
| 260 | |a Berlin, Heidelberg : |b Springer Berlin Heidelberg. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 1 | |a Lecture Notes in Mathematics |v 2054 |x 1617-9692 | |
| 500 | |a L'impression du document génère 257 p. | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliogr. Index | ||
| 505 | 1 | |a Part I Foundations of Sections 1 Continuous Non-abelian H1 with Profinite Coefficients.-2 The Fundamental Groupoid 3 Basic Geometric Operations in Terms of Sections 4 The Space of Sections as a Topological Space 5 Evaluation of Units 6 Cycle Classes in Anabelian Geometry 7 Injectivity in the Section Conjecture Part II Basic Arithmetic of Sections 7 Injectivity in the Section Conjecture 8 Reduction of Sections 9 The Space of Sections in the Arithmetic Case and the Section Conjecture in Covers Part III On the Passage from Local to Global 10 Local Obstructions at a p-adic Place 11 Brauer-Manin and Descent Obstructions 12 Fragments of Non-abelian Tate Poitou Duality Part IV Analogues of the Section Conjecture 13 On the Section Conjecture for Torsors 14 Nilpotent Sections 15 Sections over Finite Fields 16 On the Section Conjecture over Local Fields 17 Fields of Cohomological Dimension 1 18 Cuspidal Sections and Birational Analogues | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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 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 the only one against rational points on curves. This monograph begins by laying the foundations for the space of sections of the fundamental group extension of an algebraic variety. Then, arithmetic assumptions on the base field are imposed and the local-to-global approach is studied in detail. The monograph concludes by discussing analogues of the section conjecture created by varying the base field or the type of variety, or by using a characteristic quotient or its birational analogue in lieu of the fundamental group extension | ||
| 650 | |a Nombres, Théorie des | ||
| 650 | |a Géométrie algébrique | ||
| 776 | 0 | |0 165731532 |t Rational points and arithmetic of fundamental groups |o evidence for the section conjecture |f Jakob Stix |c Berlin |n Springer |d 2013 |p 1 vol. (XX-249 p.) |s Lecture notes in mathematics |z 978-3-642-30673-0 | |
| 776 | 0 | |0 165731532 |t Rational points and arithmetic of fundamental groups |o evidence for the section conjecture |f Jakob Stix |c Berlin |n Springer |d 2013 |p 1 vol. (XX-249 p.) |s Lecture notes in mathematics |z 978-3-642-30673-0 | |
| 776 | 0 | |t Rational Points and Arithmetic of Fundamental Groups |b Texte imprimé |z 9783642306754 | |
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