LEADER 04082nam 22005775 450 001 996466481603316 005 20200702151804.0 010 $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 $a20121026d2013 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aRational Points and Arithmetic of Fundamental Groups$b[electronic resource] $eEvidence for the Section Conjecture /$fby Jakob Stix 205 $a1st ed. 2013. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2013. 215 $a1 online resource (XX, 249 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$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,$x0075-8434 ;$v2054 606 $aAlgebraic geometry 606 $aNumber theory 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 615 0$aAlgebraic geometry. 615 0$aNumber theory. 615 14$aAlgebraic Geometry. 615 24$aNumber Theory. 676 $a516.35 686 $a14H30$a14G05$a14H25$a11G20$a14G32$a14F35$2msc 700 $aStix$b Jakob$4aut$4http://id.loc.gov/vocabulary/relators/aut$0479682 906 $aBOOK 912 $a996466481603316 996 $aRational points and Arithmetic of fundamental groups$9258665 997 $aUNISA LEADER 01401nam 2200433I 450 001 9910709990703321 005 20180820131500.0 035 $a(CKB)5470000002474356 035 $a(OCoLC)1048898343 035 $a(EXLCZ)995470000002474356 100 $a20180820j198210 ua 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFlexible radiator thermal vacuum test report /$fJ.A. Oren 210 1$a[Houston, Texas] :$cNational Aeronautics and Space Administration, Johnson Space Center,$d[October 1982] 215 $a1 online resource (iii, 97 pages) $cillustrations 225 1 $aNASA/CR ;$v171764 320 $aIncludes bibliographical references (page 77). 606 $aHeat radiators$2nasat 606 $aEnvironmental tests$2nasat 606 $aThermal vacuum tests$2nasat 606 $aLow Earth orbits$2nasat 606 $aStainless steels$2nasat 615 7$aHeat radiators. 615 7$aEnvironmental tests. 615 7$aThermal vacuum tests. 615 7$aLow Earth orbits. 615 7$aStainless steels. 700 $aOren$b J. A.$01411884 712 02$aLyndon B. Johnson Space Center, 801 0$bGPO 801 1$bGPO 906 $aBOOK 912 $a9910709990703321 996 $aFlexible radiator thermal vacuum test report$93504033 997 $aUNINA