LEADER 04578nam 22007695 450 001 9910299991003321 005 20200701072516.0 010 $a3-0348-0853-4 024 7 $a10.1007/978-3-0348-0853-8 035 $a(CKB)3710000000306086 035 $a(SSID)ssj0001386344 035 $a(PQKBManifestationID)11759668 035 $a(PQKBTitleCode)TC0001386344 035 $a(PQKBWorkID)11374068 035 $a(PQKB)11631387 035 $a(DE-He213)978-3-0348-0853-8 035 $a(MiAaPQ)EBC6314779 035 $a(MiAaPQ)EBC5587036 035 $a(Au-PeEL)EBL5587036 035 $a(OCoLC)1066193731 035 $a(PPN)183095464 035 $a(EXLCZ)993710000000306086 100 $a20141113d2014 u| 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aArithmetic Geometry over Global Function Fields /$fby Gebhard Böckle, David Burns, David Goss, Dinesh Thakur, Fabien Trihan, Douglas Ulmer ; edited by Francesc Bars, Ignazio Longhi, Fabien Trihan 205 $a1st ed. 2014. 210 1$aBasel :$cSpringer Basel :$cImprint: Birkhäuser,$d2014. 215 $a1 online resource (XIV, 337 p.) 225 1 $aAdvanced Courses in Mathematics - CRM Barcelona,$x2297-0304 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-0348-0852-6 327 $aCohomological Theory of Crystals over Function Fields and Applications -- On Geometric Iwasawa Theory and Special Values of Zeta Functions -- The Ongoing Binomial Revolution -- Arithmetic of Gamma, Zeta and Multizeta Values for Function Fields -- Curves and Jacobians over Function Fields. 330 $aThis volume collects the texts of five courses given in the Arithmetic Geometry Research Programme 2009?2010 at the CRM Barcelona. All of them deal with characteristic p global fields; the common theme around which they are centered is the arithmetic of L-functions (and other special functions), investigated in various aspects. Three courses examine some of the most important recent ideas in the positive characteristic theory discovered by Goss (a field in tumultuous development, which is seeing a number of spectacular advances): they cover respectively crystals over function fields (with a number of applications to L-functions of t-motives), gamma and zeta functions in characteristic p, and the binomial theorem. The other two are focused on topics closer to the classical theory of abelian varieties over number fields: they give respectively a thorough introduction to the arithmetic of Jacobians over function fields (including the current status of the BSD conjecture and its geometric analogues, and the construction of Mordell?Weil groups of high rank) and a state of the art survey of Geometric Iwasawa Theory explaining the recent proofs of various versions of the Main Conjecture, in the commutative and non-commutative settings. 410 0$aAdvanced Courses in Mathematics - CRM Barcelona,$x2297-0304 606 $aNumber theory 606 $aAlgebra 606 $aAlgebraic geometry 606 $aNumber Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M25001 606 $aGeneral Algebraic Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/M1106X 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 615 0$aNumber theory. 615 0$aAlgebra. 615 0$aAlgebraic geometry. 615 14$aNumber Theory. 615 24$aGeneral Algebraic Systems. 615 24$aAlgebraic Geometry. 676 $a512.7 700 $aBöckle$b Gebhard$4aut$4http://id.loc.gov/vocabulary/relators/aut$01065141 702 $aBurns$b David$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aGoss$b David$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aThakur$b Dinesh$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aTrihan$b Fabien$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aUlmer$b Douglas$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aBars$b Francesc$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aLonghi$b Ignazio$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aTrihan$b Fabien$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299991003321 996 $aArithmetic Geometry over Global Function Fields$92543320 997 $aUNINA