Galois Module Structure (Fields Institute Monographs)

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9780821802649: Galois Module Structure (Fields Institute Monographs)

Galois module structure deals with the construction of algebraic invariants from a Galois extension of number fields with group $G$. Typically these invariants lie in the class-group of some group-ring of $G$ or of a related order. These class-groups have ``Hom-descriptions'' in terms of idelic-valued functions on the complex representations of $G$. Following a theme pioneered by A. Frolich, T. Chinburg constructed several invariants whose Hom-descriptions are (conjecturally) given in terms of Artin root numbers. For a tame extension, the second Chinburg invariant is given by the ring of integers, and M. J. Taylor proved the conjecture in this case. The first published graduate course on the Chinburg conjectures, this book provides the necessary background in algebraic and analytic number theory, cohomology, representation theory, and Hom-descriptions. The computation of Hom-descriptions is facilitated by Snaith's Explicit Brauer Induction technique in representation theory. In this way, illustrative special cases of the main results and new examples of the conjectures are proved and amplified by numerous exercises and research problems. The final chapter introduces a new invariant constructed from algebraic $K$-theory, whose Hom-description is related to the $L$-function value at $s = -1$.

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It will be useful for specialists inside and outside of this subject, as well as for graduate students. --Zentralblatt für Mathematik

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1.

Victor P. Snaith
Editorial: American Mathematical Society, Fields Institute (1994)
ISBN 10: 082180264X ISBN 13: 9780821802649
Nuevos Tapa dura Cantidad: > 20
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Sequitur Books
(Boonsboro, MD, Estados Unidos de America)
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Descripción American Mathematical Society, Fields Institute, 1994. Hardcover. Estado de conservación: New. Brand new. We distribute directly for the publisher. Galois module structure deals with the construction of algebraic invariants from a Galois extension of number fields with group $G$. Typically these invariants lie in the class-group of some group-ring of $G$ or of a related order. These class-groups have "Hom-descriptions" in terms of idèlic-valued functions on the complex representations of $G$. Following a theme pioneered by A. Frölich, T. Chinburg constructed several invariants whose Hom-descriptions are (conjecturally) given in terms of Artin root numbers. For a tame extension, the second Chinburg invariant is given by the ring of integers, and M. J. Taylor proved the conjecture in this case. The first published graduate course on the Chinburg conjectures, this book provides the necessary background in algebraic and analytic number theory, cohomology, representation theory, and Hom-descriptions. The computation of Hom-descriptions is facilitated by Snaith's Explicit Brauer Induction technique in representation theory. In this way, illustrative special cases of the main results and new examples of the conjectures are proved and amplified by numerous exercises and research problems. The final chapter introduces a new invariant constructed from algebraic $K$-theory, whose Hom-description is related to the $L$-function value at $s = -1$. Nº de ref. de la librería 1007130018

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Victor P. Snaith
Editorial: American Mathematical Society, United States (1995)
ISBN 10: 082180264X ISBN 13: 9780821802649
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Descripción American Mathematical Society, United States, 1995. Hardback. Estado de conservación: New. Language: English . Brand New Book. Galois module structure deals with the construction of algebraic invariants from a Galois extension of number fields with group $G$. Typically these invariants lie in the class-group of some group-ring of $G$ or of a related order. These class-groups have Hom-descriptions in terms of idelic-valued functions on the complex representations of $G$. Following a theme pioneered by A. Frolich, T. Chinburg constructed several invariants whose Hom-descriptions are (conjecturally) given in terms of Artin root numbers. For a tame extension, the second Chinburg invariant is given by the ring of integers, and M. J. Taylor proved the conjecture in this case.The first published graduate course on the Chinburg conjectures, this book provides the necessary background in algebraic and analytic number theory, cohomology, representation theory, and Hom-descriptions. The computation of Hom-descriptions is facilitated by Snaith s Explicit Brauer Induction technique in representation theory. In this way, illustrative special cases of the main results and new examples of the conjectures are proved and amplified by numerous exercises and research problems.The final chapter introduces a new invariant constructed from algebraic $K$-theory, whose Hom-description is related to the $L$-function value at $s = -1$. Nº de ref. de la librería AAN9780821802649

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Victor P. Snaith
Editorial: American Mathematical Society, Fields Institute (1994)
ISBN 10: 082180264X ISBN 13: 9780821802649
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Descripción American Mathematical Society, Fields Institute, 1994. Hardcover. Estado de conservación: New. book. Nº de ref. de la librería 082180264X

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Victor P. Snaith
Editorial: American Mathematical Society, Fields Institute (1994)
ISBN 10: 082180264X ISBN 13: 9780821802649
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Descripción American Mathematical Society, Fields Institute, 1994. Hardcover. Estado de conservación: New. Nº de ref. de la librería DADAX082180264X

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Victor P. Snaith
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Descripción American Mathematical Society, United States, 1995. Hardback. Estado de conservación: New. Language: English . Brand New Book. Galois module structure deals with the construction of algebraic invariants from a Galois extension of number fields with group $G$. Typically these invariants lie in the class-group of some group-ring of $G$ or of a related order. These class-groups have Hom-descriptions in terms of idelic-valued functions on the complex representations of $G$. Following a theme pioneered by A. Frolich, T. Chinburg constructed several invariants whose Hom-descriptions are (conjecturally) given in terms of Artin root numbers. For a tame extension, the second Chinburg invariant is given by the ring of integers, and M. J. Taylor proved the conjecture in this case.The first published graduate course on the Chinburg conjectures, this book provides the necessary background in algebraic and analytic number theory, cohomology, representation theory, and Hom-descriptions. The computation of Hom-descriptions is facilitated by Snaith s Explicit Brauer Induction technique in representation theory. In this way, illustrative special cases of the main results and new examples of the conjectures are proved and amplified by numerous exercises and research problems.The final chapter introduces a new invariant constructed from algebraic $K$-theory, whose Hom-description is related to the $L$-function value at $s = -1$. Nº de ref. de la librería AAN9780821802649

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Victor P. Snaith
ISBN 10: 082180264X ISBN 13: 9780821802649
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Descripción Estado de conservación: New. Bookseller Inventory # ST082180264X. Nº de ref. de la librería ST082180264X

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Victor P. Snaith
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Descripción American Mathematical Society. Hardback. Estado de conservación: new. BRAND NEW, Galois Module Structure, Victor P. Snaith, Galois module structure deals with the construction of algebraic invariants from a Galois extension of number fields with group $G$. Typically these invariants lie in the class-group of some group-ring of $G$ or of a related order. These class-groups have 'Hom-descriptions' in terms of idelic-valued functions on the complex representations of $G$. Following a theme pioneered by A. Frolich, T. Chinburg constructed several invariants whose Hom-descriptions are (conjecturally) given in terms of Artin root numbers. For a tame extension, the second Chinburg invariant is given by the ring of integers, and M. J. Taylor proved the conjecture in this case.The first published graduate course on the Chinburg conjectures, this book provides the necessary background in algebraic and analytic number theory, cohomology, representation theory, and Hom-descriptions. The computation of Hom-descriptions is facilitated by Snaith's Explicit Brauer Induction technique in representation theory. In this way, illustrative special cases of the main results and new examples of the conjectures are proved and amplified by numerous exercises and research problems. The final chapter introduces a new invariant constructed from algebraic $K$-theory, whose Hom-description is related to the $L$-function value at $s = -1$. Nº de ref. de la librería B9780821802649

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Victor P. Snaith
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Descripción Estado de conservación: New. Depending on your location, this item may ship from the US or UK. Nº de ref. de la librería 97808218026490000000

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Victor P. Snaith
Editorial: Amer Mathematical Society (1995)
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Descripción Amer Mathematical Society, 1995. Hardcover. Estado de conservación: Brand New. first edition edition. 207 pages. 10.50x7.25x0.75 inches. In Stock. Nº de ref. de la librería __082180264X

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Victor P. Snaith
Editorial: American Mathematical Society, Fields Institute (1994)
ISBN 10: 082180264X ISBN 13: 9780821802649
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Descripción American Mathematical Society, Fields Institute, 1994. Estado de conservación: New. Galois module structure deals with the construction of algebraic invariants from a Galois extension of number fields with group $G$. This title addresses the Chinburg conjectures. It provides the background in algebraic and analytic number theory, cohomology, representation theory, and Hom-descriptions. Series: Fields Institute Monographs. Num Pages: 207 pages, index, bibliography. BIC Classification: PBF; PBH. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 267 x 184. Weight in Grams: 567. . 1994. 0th Edition. Hardcover. . . . . . Nº de ref. de la librería V9780821802649

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