LEADER 04014nam 2200637Ia 450 001 9910438158703321 005 20200520144314.0 010 $a3-642-30674-8 024 7 $a10.1007/978-3-642-30674-7 035 $a(CKB)3400000000102743 035 $a(SSID)ssj0000788855 035 $a(PQKBManifestationID)11429413 035 $a(PQKBTitleCode)TC0000788855 035 $a(PQKBWorkID)10847623 035 $a(PQKB)11436668 035 $a(DE-He213)978-3-642-30674-7 035 $a(MiAaPQ)EBC3070837 035 $a(PPN)168317397 035 $a(EXLCZ)993400000000102743 100 $a20120730d2013 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aRational points and arithmetic of fundamental groups $eevidence for the section conjecture /$fJakob Stix 205 $a1st ed. 2013. 210 $aBerlin ;$aNew York $cSpringer$dc2013 215 $a1 online resource (XX, 249 p.) 225 1 $aLecture notes in mathematics,$x1617-9692 ;$v2054 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-642-30673-X 320 $aIncludes bibliographical references (p. [239]-245) and index. 327 $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. 330 $aThe section conjecture in anabelian geometry, announced by Grothendieck in 1983, is concerned with a description of the set of rational points of a hyperbolic algebraic curve over a number field in terms of the arithmetic of its fundamental group. While the conjecture is still open today in 2012, its study has revealed interesting arithmetic for curves and opened connections, for example, to the question whether the Brauer-Manin obstruction is the only one against rational points on curves. This monograph begins by laying the foundations for the space of sections of the fundamental group extension of an algebraic variety. Then, arithmetic assumptions on the base field are imposed and the local-to-global approach is studied in detail. The monograph concludes by discussing analogues of the section conjecture created by varying the base field or the type of variety, or by using a characteristic quotient or its birational analogue in lieu of the fundamental group extension. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v2054. 606 $aRational points (Geometry) 606 $aFundamental groups (Mathematics) 606 $aGeometry, Algebraic 606 $aNon-Abelian groups 606 $aNumber theory 615 0$aRational points (Geometry) 615 0$aFundamental groups (Mathematics) 615 0$aGeometry, Algebraic. 615 0$aNon-Abelian groups. 615 0$aNumber theory. 676 $a516.35 686 $a14H30$a14G05$a14H25$a11G20$a14G32$a14F35$2msc 700 $aStix$b Jakob$0479682 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910438158703321 996 $aRational points and Arithmetic of fundamental groups$9258665 997 $aUNINA