000			04098nam a22005415i 4500
001			978-0-8176-4515-1
003			DE-He213
005			20251006084435.0
007			cr nn 008mamaa
008			100301s2006 xxu| s |||| 0|eng d
020			_a9780817645151
020			_a99780817645151
024	7		_a10.1007/0-8176-4515-2 _2doi
082	0	4	_a512.7 _223
100	1		_aVilla Salvador, Gabriel Daniel. _eauthor.
245	1	0	_aTopics in the Theory of Algebraic Function Fields _h[electronic resource] / _cby Gabriel Daniel Villa Salvador.
264		1	_aBoston, MA : _bBirkhäuser Boston, _c2006.
300			_aXVI, 652 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aMathematics: Theory & Applications
505	0		_aAlgebraic and Numerical Antecedents -- Algebraic Function Fields of One Variable -- The Riemann-Roch Theorem -- Examples -- Extensions and Galois Theory -- Congruence Function Fields -- The Riemann Hypothesis -- Constant and Separable Extensions -- The Riemann-Hurwitz Formula -- Cryptography and Function Fields -- to Class Field Theory -- Cyclotomic Function Fields -- Drinfeld Modules -- Automorphisms and Galois Theory.
520			_aThe fields of algebraic functions of one variable appear in several areas of mathematics: complex analysis, algebraic geometry, and number theory. This text adopts the latter perspective by applying an arithmetic-algebraic viewpoint to the study of function fields as part of the algebraic theory of numbers, where a function field of one variable is the analogue of a finite extension of Q, the field of rational numbers. The author does not ignore the geometric-analytic aspects of function fields, but leaves an in-depth examination from this perspective to others. Key topics and features: * Contains an introductory chapter on algebraic and numerical antecedents, including transcendental extensions of fields, absolute values on Q, and Riemann surfaces * Focuses on the Riemann-Roch theorem, covering divisors, adeles or repartitions, Weil differentials, class partitions, and more * Includes chapters on extensions, automorphisms and Galois theory, congruence function fields, the Riemann Hypothesis, the Riemann-Hurwitz Formula, applications of function fields to cryptography, class field theory, cyclotomic function fields, and Drinfeld modules * Explains both the similarities and fundamental differences between function fields and number fields * Includes many exercises and examples to enhance understanding and motivate further study The only prerequisites are a basic knowledge of field theory, complex analysis, and some commutative algebra. The book can serve as a text for a graduate course in number theory or an advanced graduate topics course. Alternatively, chapters 1-4 can serve as the base of an introductory undergraduate course for mathematics majors, while chapters 5-9 can support a second course for advanced undergraduates. Researchers interested in number theory, field theory, and their interactions will also find the work an excellent reference.
650		0	_aMATHEMATICS.
650		0	_aGEOMETRY, ALGEBRAIC.
650		0	_aALGEBRA.
650		0	_aFIELD THEORY (PHYSICS).
650		0	_aGLOBAL ANALYSIS (MATHEMATICS).
650		0	_aFUNCTIONS OF COMPLEX VARIABLES.
650		0	_aNUMBER THEORY.
650	1	4	_aMATHEMATICS.
650	2	4	_aNUMBER THEORY.
650	2	4	_aFUNCTIONS OF A COMPLEX VARIABLE.
650	2	4	_aALGEBRAIC GEOMETRY.
650	2	4	_aFIELD THEORY AND POLYNOMIALS.
650	2	4	_aANALYSIS.
650	2	4	_aCOMMUTATIVE RINGS AND ALGEBRAS.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780817644802
830		0	_aMathematics: Theory & Applications
856	4	0	_uhttp://dx.doi.org/10.1007/0-8176-4515-2 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c59678 _d59678