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001 978-3-642-30674-7
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008 121026s2013 gw | s |||| 0|eng d
020 _a9783642306747
_9978-3-642-30674-7
024 7 _a10.1007/978-3-642-30674-7
_2doi
050 4 _aQA564-609
072 7 _aPBMW
_2bicssc
072 7 _aMAT012010
_2bisacsh
072 7 _aPBMW
_2thema
082 0 4 _a516.35
_223
100 1 _aStix, Jakob.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aRational Points and Arithmetic of Fundamental Groups
_h[electronic resource] :
_bEvidence for the Section Conjecture /
_cby Jakob Stix.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c2013.
300 _aXX, 249 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2054
505 0 _aPart 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.
520 _aThe 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 0 _aGeometry, algebraic.
650 0 _aNumber theory.
650 1 4 _aAlgebraic Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M11019
650 2 4 _aNumber Theory.
_0http://scigraph.springernature.com/things/product-market-codes/M25001
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642306730
776 0 8 _iPrinted edition:
_z9783642306754
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2054
856 4 0 _uhttps://doi.org/10.1007/978-3-642-30674-7
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c11650
_d11650