Rational points and arithmetic of fundamental groups [Documento electrónico] : evidence for the section conjecture / Jakob Stix
Language: eng.Country: Germany.Publication: Berlin, Heidelberg : Springer Berlin Heidelberg, 2013Description: XX, 249 p.ISBN: 978-3-642-30674-7.Series: Lecture Notes in MathematicsSubject - Topical Name: Geometria algébrica Online Resources:Click here to access online| Item type | Current library | Collection | Call number | Copy number | Status | Date due | Barcode | |
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| QA564.SPR FCT 82392 Shapes and diffeomorphisms | QA564.SPR FCT 82458 Arithmetic geometry, lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 10-15, 2007 | QA564.SPR FCT 82492 Homogeneous spaces and equivariant embeddings | QA564.SPR FCT 82553 Rational points and arithmetic of fundamental groups, evidence for the section conjecture | QA564.SPR FCT 82635 Nonabelian jacobian of projective surfaces, geometry and representation theory | QA564.SPR FCT 82640 Real algebraic geometry | QA564.SPR FCT 82658 Basic algebraic geometry 1, varieties in projective space |
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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.
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