Book contents
- Frontmatter
- Contents
- List of contributors
- Preface
- PART ONE LECTURE NOTES
- PART TWO CONTRIBUTED PAPERS
- 4 Torsors over Luna strata
- 5 Abélianisation des espaces homogènes et applications arithmétiques
- 6 Gaussian rational points on a singular cubic surface
- 7 Actions algébriques de groupes arithmétiques
- 8 Descent theory for open varieties
- 9 Homotopy obstructions to rational points
- 10 Factorially graded rings of complexity one
- 11 Nef and semiample divisors on rational surfaces
- References
9 - Homotopy obstructions to rational points
from PART TWO - CONTRIBUTED PAPERS
Published online by Cambridge University Press: 05 May 2013
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Book contents
- Frontmatter
- Contents
- List of contributors
- Preface
- PART ONE LECTURE NOTES
- PART TWO CONTRIBUTED PAPERS
- 4 Torsors over Luna strata
- 5 Abélianisation des espaces homogènes et applications arithmétiques
- 6 Gaussian rational points on a singular cubic surface
- 7 Actions algébriques de groupes arithmétiques
- 8 Descent theory for open varieties
- 9 Homotopy obstructions to rational points
- 10 Factorially graded rings of complexity one
- 11 Nef and semiample divisors on rational surfaces
- References
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- Torsors, Étale Homotopy and Applications to Rational Points , pp. 280 - 413Publisher: Cambridge University PressPrint publication year: 2013
References
[AMa69] , , Étale Homotopy, Lecture Notes in Mathematics, 100, 1969.
[Bro73] , Abstract homotopy theory and generalized sheaf cohomology, Transactions of the American Mathematical Society, 186, 1973, p. 419–458.Google Scholar
[BSc11] , , A projective model structure on pro simplicial sheaves, and the relative étale homotopy type, preprint http://arxiv.org/pdf/1109.5477.pdf.
[BSe64] , , Théorèmes de finitude en cohomologie galoisienne, Commentarii Mathematici Helvetici, 39(1), 1964, p. 111–164.Google Scholar
[CTS80] , , La descente sur les variétés rationnelles, Journées de Géométrie Algébrique d'Angers, Juillet 1979, p. 223–237.
[CTS87] , , La descente sur les variétés rationnelles II, Duke Mathematical Journal, 54 (2), 1987, p. 375–492.Google Scholar
[De09a] , Obstruction de descente et obstruction de Brauer-Manin étale, Algebra and Number Theory, 3 (2), 2009, p. 237–254.Google Scholar
[De09b] , Théorèmes de dualité pour les complexes de tores, preprint, 2009, http://arxiv.org/abs/0906.3453v1.
[Dol58] , Homology of symmetric products and other functors of complexes, Annals of Mathematics, 68 (1), 1958.Google Scholar
[EHa76] , . Cech and Steenrod homotopy theories with applications to geometric topology, Lecture Notes in Mathematics, 542, Springer Verlag, 1976.
[FIs07] , , Model structures on pro-categories, Homology, Homotopy and Applications, 9 (1), 2007, p. 367–398.Google Scholar
[Fri82] , Étale homotopy of simplicial schemes, Annals of Mathematics Studies, 104, Princeton University Press, 1982.
[GJa99] , . Simplicial Homotopy Theory, Progress in Mathematics, 174, Birkhäuser, 1999.
[Goe95] , Homotopy fixed points for Galois groups, Contemporary Mathematics, 181, p. 187–224.
[Har02] , Groupes algébriques et points rationnels, Mathematische Annalen, 322 (4), 2002, p. 811–826.Google Scholar
[HSk02] , , Non-abelian cohomology and rational points, Compositio Mathematica, 130 (3), 2002, p. 241–273.Google Scholar
[HSz05] , , Arithmetic duality theorems for 1-motives, Journal für die reine und angewandte Mathematik, 578, 2005, p. 93–128.Google Scholar
[Isk71] , A counterexample to the Hasse principle for systems of two quadratic forms in five variables, Mathematical Notes, 10 (3), 1971, p. 575–577.Google Scholar
[Jar87] , Simplicial Presheaves, Journal of Pure and Applied Algebra, 47, 1987, p. 35–87.Google Scholar
[Jos09] , The Arithmetic of 1-motives, Thesis, Central European University, 2009.
[Lie08] , Twisted sheaves and the period-index problem, Compositio Mathematica, 144, 2008, p. 1–31.Google Scholar
[Lin40] , Untersuchungen über die rationalen Punkte der ebenen kubischen Kurven vom Geschlecht Eins, Thesis, University of Uppsala, 1940.
[Man70] , Le groupe de Brauer-Grothendieck en géométrie dio-phantienne, Actes du Congrès International Des Mathématiciens, Tome 1, 1970, p. 401–411.
[Mil06] , Arithmetic Duality Theorems, 2nd ed., BookSurge, LLC., 2006.
[Pal10] , Homotopy sections and rational points on algebraic varieties, http://arxiv.org/abs/1002.1731, preprint, 2010.
[Poo10] , Insufficiency of the Brauer-Manin obstruction applied to étale covers, Ann. of Math. 171, 2010, p. 2157–2169.Google Scholar
[Qui09] , Continuous group actions on profinite spaces, Journal of Pure and Applied Algebra, 215, 2011, p. 1024–1039.Google Scholar
[Rei42] , Einige im Kleinen überall lösbare, im Grossen unlösbare diophantische Gleichungen, Journal für die reine und angewandte Mathematik, 184, 1942, p. 12–18.Google Scholar
[Sch09] , On the Brauer-Manin obstruction applied to ramified covers, preprint, 2009, http://arxiv.org/abs/0911.5728.
[SGA4] , , , Théorie des Topos et Cohomologie Étale des Schémas, Lecture Notes in Math. 270, Springer, 1972.
[Sko99] , Beyond the Manin obstruction, Inventiones Mathematicae, 135 (2), 1999, p. 399–424.Google Scholar
[Sko01] , Torsors and Rational Points, Cambridge University Press, 2001.
[Sko09] , Descent obstruction is equivalent to étale Brauer-Manin obstruction, Mathematische Annalen, 344 (3), 2009, p. 501–510.Google Scholar
[Spa88] , Resolutions of unbounded complexes, Compositio Mathematica, 65 (2), 1988, p. 121–154.Google Scholar
[Sto07] , Finite descent obstructions and rational points on curves, Algebra and Number Theory, 1 (4), 2007, p. 349–391.Google Scholar
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