02814nmm a2200361 u 4500001001200000003002700012005001700039007002400056008004100080020001800121100002100139245022400160250001700384260003500401300003200436505029300468653001800761653002300779653003000802653001800832653002200850653002300872700002700895700002600922700002900948041001900977989003600996490005201032028003001084856007201114082001001186520125601196EB000901600EBX0100000000000000069817100000000000000.0cr|||||||||||||||||||||141202 ||| eng a97830348085381 aBöckle, Gebhard00aArithmetic Geometry over Global Function FieldshElektronische Ressourcecby Gebhard Böckle, David Burns, David Goss, Dinesh Thakur, Fabien Trihan, Douglas Ulmer ; edited by Francesc Bars, Ignazio Longhi, Fabien Trihan a1st ed. 2014 aBaselbBirkhäuserc2014, 2014 aXIV, 337 pbonline resource0 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 aNumber theory aAlgebraic Geometry aGeneral Algebraic Systems aNumber Theory aUniversal algebra aAlgebraic geometry1 aBurns, Davide[author]1 aGoss, Davide[author]1 aThakur, Dineshe[author]07aeng2ISO 639-2 bSpringeraSpringer eBooks 2005-0 aAdvanced Courses in Mathematics - CRM Barcelona50a10.1007/978-3-0348-0853-840uhttps://doi.org/10.1007/978-3-0348-0853-8?nosfx=yxVerlag3Volltext0 a512.7 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