Algebraische Zahlentheorie (Springer-Lehrbuch Masterclass) by Jürgen Neukirch PDF

By Jürgen Neukirch

ISBN-10: 3540375473

ISBN-13: 9783540375470

Algebraische Zahlentheorie: eine der traditionsreichsten und aktuellsten Grunddisziplinen der Mathematik. Das vorliegende Buch schildert ausführlich Grundlagen und Höhepunkte. Konkret, smooth und in vielen Teilen neu. Neu: Theorie der Ordnungen. Plus: die geometrische Neubegründung der Theorie der algebraischen Zahlkörper durch die "Riemann-Roch-Theorie" vom "Arakelovschen Standpunkt", die bis hin zum "Grothendieck-Riemann-Roch-Theorem" führt.

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Extra resources for Algebraische Zahlentheorie (Springer-Lehrbuch Masterclass)

Sample text

D(a,r -), resp. C(a,r) denotes the Cl1"C1Jmjerenced disk {x E Kllx - al ~ r} (resp. the non-circumferenced disk {x E 1<1 Ix - al < r}, resp. the circle {x E KJ Ix - 01 = r} ). We call a class 01 d(a , r) any non-circumferenced disk d(b,r - ) with la - bl:S: r. Let r' > 0 and T" > r', r(a,r',r") denotes the annulus {x E KI r' < Ix - at < G iven A, B C K, we denote by 6(A,8) the distance from A to 8. Also diam(A) denotes the diameter of A. rill . Let D be an infinite set in K, and let a ED. If D is bounded of diameter ", we denote by iJ the disk d(a, r), and if D is not bounded, we put jj == K.

M)' m,N If a monotonous holes sequence of diameter r has an inferior limit-piercing p > 0 and a superior limit-piercing pi < r, it is called correctly TJierced. A set D is said to be correctly pierced if every monotonous distances holes sequence of D with a nOll empty D-beach js correctly pierced . e. the set of diameters of the holes of D has a str ictly positive lower bound. ~ . Cm) a sequence of nOIl- "'- EN ncgative integers. ,q"",) I$ . (",). I! < . ' = 1 for infin itely many (m , i) . {m) be an increasing (resp.

N,}) Ib"". - bn ,)! ,) I < .

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