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Arithmetic geometry over global function fields [electronic resource]

Arithmetic geometry over global function fields [electronic resource]

자료유형
E-Book(소장)
개인저자
Böckle, Gebhard. Bars, Francesc. Longhi, Ignazio. Trihan, Fabien.
서명 / 저자사항
Arithmetic geometry over global function fields [electronic resource] / Gebhard Böckle ... [et al.] ; Francesc Bars, Ignazio Longhi, Fabien Trihan, editor.
발행사항
Basel :   Springer Basel :   Birkhäuser,   2014.  
형태사항
1 online resource (xiv, 337 p.).
총서사항
Advanced courses in mathematics, CRM Barcelona,2297-0304
ISBN
9783034808538
요약
This 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.
일반주기
Title from e-Book title page.  
내용주기
Cohomological 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.
서지주기
Includes bibliographical references.
이용가능한 다른형태자료
Issued also as a book.  
일반주제명
Mathematics. Geometry, Algebraic. Algebra. Number theory.
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020 ▼a 9783034808538
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245 0 0 ▼a Arithmetic geometry over global function fields ▼h [electronic resource] / ▼c Gebhard Böckle ... [et al.] ; Francesc Bars, Ignazio Longhi, Fabien Trihan, editor.
260 ▼a Basel : ▼b Springer Basel : ▼b Birkhäuser, ▼c 2014.
300 ▼a 1 online resource (xiv, 337 p.).
490 1 ▼a Advanced courses in mathematics, CRM Barcelona, ▼x 2297-0304
500 ▼a Title from e-Book title page.
504 ▼a Includes bibliographical references.
505 0 ▼a Cohomological 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.
520 ▼a This 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.
530 ▼a Issued also as a book.
538 ▼a Mode of access: World Wide Web.
650 0 ▼a Mathematics.
650 0 ▼a Geometry, Algebraic.
650 0 ▼a Algebra.
650 0 ▼a Number theory.
700 1 ▼a Böckle, Gebhard.
700 1 ▼a Bars, Francesc.
700 1 ▼a Longhi, Ignazio.
700 1 ▼a Trihan, Fabien.
830 0 ▼a Advanced courses in mathematics, CRM Barcelona.
856 4 0 ▼u https://oca.korea.ac.kr/link.n2s?url=http://dx.doi.org/10.1007/978-3-0348-0853-8
945 ▼a KLPA
991 ▼a E-Book(소장)

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