Galois Module Structure (Fields Institute Monographs)

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9780821802649: Galois Module Structure (Fields Institute Monographs)
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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 id\`elic-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 $s = -1$.

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Snaith, Victor P.
ISBN 10: 082180264X ISBN 13: 9780821802649
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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: American Mathematical Society, United States (1995)
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Descripción American Mathematical Society, United States, 1995. Hardback. Estado de conservación: New. 251 x 175 mm. 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, 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. 251 x 175 mm. 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
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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
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. 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
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ISBN 10: 082180264X ISBN 13: 9780821802649
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Descripción American Mathematical Society, Fields Institute, 1994. Hardcover. Estado de conservación: New. First Edition. Nº de ref. de la librería DADAX082180264X

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Victor P. Snaith
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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
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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
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Descripción 1995. Hardcover. Estado de conservación: New. 175mm x 18mm x 251mm. Hardcover. 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 so.Shipping may be from multiple locations in the US or from the UK, depending on stock availability. 207 pages. 0.567. Nº de ref. de la librería 9780821802649

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Victor P. Snaith
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Descripción 1995. Hardcover. Estado de conservación: New. 175mm x 18mm x 251mm. Hardcover. 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 clas.Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. 207 pages. 0.567. Nº de ref. de la librería 9780821802649

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