ISBN: 9781848822429
ID: 9781848822429
A Mathematician Said Who Can Quote Me a Theorem that`s True For the ones that I Know Are Simply not So, When the Characteristic is Two! This pretty limerick rst came to my ears in May 1998 during a talk by T.Y. Lam 1 on eld invariants from the theory of quadratic forms. It is-poetic exaggeration allowed-a suitable motto for this monograph. What is it about At the beginning of the seventies I drew up a specialization theoryofquadraticandsymmetricbilinear formsover elds[32].Let : K L be a place. Then one can assign a form ( )toaform over K in a meaningful way if has `good reduction` with respect to (see 1.1). The basic idea is to simply apply the place to the coe cients of , which must therefore be in the valuation ring of . The specialization theory of that time was satisfactory as long as the eld L, and therefore also K, had characteristic 2. It served me in the rst place as the foundation for a theory of generic splitting of quadratic forms [33], [34]. After a very modest beginning, this theory is now in full bloom. It became important for the understanding of quadratic forms over elds, as can be seen from the book [26]of Izhboldin-Kahn-Karpenko-Vishik for instance. One should note that there exists a theoryof(partial)genericsplittingofcentralsimplealgebrasandreductivealgebraic groups, parallel to the theory of generic splitting of quadratic forms (see [29] and the literature cited there). Specialization of Quadratic and Symmetric Bilinear Forms: A Mathematician Said Who Can Quote Me a Theorem that`s True For the ones that I Know Are Simply not So, When the Characteristic is Two! This pretty limerick rst came to my ears in May 1998 during a talk by T.Y. Lam 1 on eld invariants from the theory of quadratic forms. It is-poetic exaggeration allowed-a suitable motto for this monograph. What is it about At the beginning of the seventies I drew up a specialization theoryofquadraticandsymmetricbilinear formsover elds[32].Let : K L be a place. Then one can assign a form ( )toaform over K in a meaningful way if has `good reduction` with respect to (see 1.1). The basic idea is to simply apply the place to the coe cients of , which must therefore be in the valuation ring of . The specialization theory of that time was satisfactory as long as the eld L, and therefore also K, had characteristic 2. It served me in the rst place as the foundation for a theory of generic splitting of quadratic forms [33], [34]. After a very modest beginning, this theory is now in full bloom. It became important for the understanding of quadratic forms over elds, as can be seen from the book [26]of Izhboldin-Kahn-Karpenko-Vishik for instance. One should note that there exists a theoryof(partial)genericsplittingofcentralsimplealgebrasandreductivealgebraic groups, parallel to the theory of generic splitting of quadratic forms (see [29] and the literature cited there). DEX Generic splitting theory Quadratic forms Specialization theory Symmetric bilinear forms addition character form integral quadratic form quadratic places B Algebra Mathematics and Statistics, Springer London
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ISBN: 9781848822429
ID: 9781848822429
A Mathematician Said Who Can Quote Me a Theorem that`s True For the ones that I Know Are Simply not So, When the Characteristic is Two! This pretty limerick rst came to my ears in May 1998 during a talk by T.Y. Lam 1 on eld invariants from the theory of quadratic forms. It is-poetic exaggeration allowed-a suitable motto for this monograph. What is it about At the beginning of the seventies I drew up a specialization theoryofquadraticandsymmetricbilinear formsover elds[32].Let : K L be a place. Then one can assign a form ( )toaform over K in a meaningful way if has `good reduction` with respect to (see 1.1). The basic idea is to simply apply the place to the coe cients of , which must therefore be in the valuation ring of . The specialization theory of that time was satisfactory as long as the eld L, and therefore also K, had characteristic 2. It served me in the rst place as the foundation for a theory of generic splitting of quadratic forms [33], [34]. After a very modest beginning, this theory is now in full bloom. It became important for the understanding of quadratic forms over elds, as can be seen from the book [26]of Izhboldin-Kahn-Karpenko-Vishik for instance. One should note that there exists a theoryof(partial)genericsplittingofcentralsimplealgebrasandreductivealgebraic groups, parallel to the theory of generic splitting of quadratic forms (see [29] and the literature cited there). Specialization of Quadratic and Symmetric Bilinear Forms: A Mathematician Said Who Can Quote Me a Theorem that`s True For the ones that I Know Are Simply not So, When the Characteristic is Two! This pretty limerick rst came to my ears in May 1998 during a talk by T.Y. Lam 1 on eld invariants from the theory of quadratic forms. It is-poetic exaggeration allowed-a suitable motto for this monograph. What is it about At the beginning of the seventies I drew up a specialization theoryofquadraticandsymmetricbilinear formsover elds[32].Let : K L be a place. Then one can assign a form ( )toaform over K in a meaningful way if has `good reduction` with respect to (see 1.1). The basic idea is to simply apply the place to the coe cients of , which must therefore be in the valuation ring of . The specialization theory of that time was satisfactory as long as the eld L, and therefore also K, had characteristic 2. It served me in the rst place as the foundation for a theory of generic splitting of quadratic forms [33], [34]. After a very modest beginning, this theory is now in full bloom. It became important for the understanding of quadratic forms over elds, as can be seen from the book [26]of Izhboldin-Kahn-Karpenko-Vishik for instance. One should note that there exists a theoryof(partial)genericsplittingofcentralsimplealgebrasandreductivealgebraic groups, parallel to the theory of generic splitting of quadratic forms (see [29] and the literature cited there). MATHEMATICS / Algebra / General, Springer-Verlag Gmbh
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ISBN: 9781848822429
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A Mathematician Said Who Can Quote Me a Theorem that's True? For the ones that I Know Are Simply not So, When the Characteristic is Two! This pretty limerick? rst came to my ears in May 1998 during a talk by T.Y. Lam 1 on? eld invariants from the theory of quadratic forms. It is-poetic exaggeration allowed-a suitable motto for this monograph. What is it about? At the beginning of the seventies I drew up a specialization theoryofquadraticandsymmetricbilinear formsover? elds[32].Let? : K? L be a A Mathematician Said Who Can Quote Me a Theorem that's True? For the ones that I Know Are Simply not So, When the Characteristic is Two! This pretty limerick? rst came to my ears in May 1998 during a talk by T.Y. Lam 1 on? eld invariants from the theory of quadratic forms. It is-poetic exaggeration allowed-a suitable motto for this monograph. What is it about? At the beginning of the seventies I drew up a specialization theoryofquadraticandsymmetricbilinear formsover? elds[32].Let? : K? L be a place. Then one can assign a form? (?)toaform? over K in a meaningful way? if? has "good reduction" with respect to? (see 1.1). The basic idea is to simply apply the place? to the coe?cients of? which must therefore be in the valuation ring of? The specialization theory of that time was satisfactory as long as the? eld L, and therefore also K, had characteristic 2. It served me in the? rst place as the foundation for a theory of generic splitting of quadratic forms [33], [34]. After a very modest beginning, this theory is now in full bloom. It became important for the understanding of quadratic forms over? elds, as can be seen from the book [26]of Izhboldin-Kahn-Karpenko-Vishik for instance. One should note that there exists a theoryof(partial)genericsplittingofcentralsimplealgebrasandreductivealgebraic groups, parallel to the theory of generic splitting of quadratic forms (see [29] and the literature cited there). Algebra, Mathematics, Specialization of Quadratic and Symmetric Bilinear Forms~~ Manfred Knebusch, Thomas Unger~~Algebra~~Mathematics~~9781848822429, en, Specialization of Quadratic and Symmetric Bilinear Forms, Manfred Knebusch, Thomas Unger, 9781848822429, Springer, 01/22/2011, , , , Springer, 01/22/2011
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2011, ISBN: 1848822421
ID: 9781848822429
In englischer Sprache. Verlag: Springer London, A Mathematician Said Who Can Quote Me a Theorem that?s True? For the ones that I Know Are Simply not So, When the Characteristic is Two! This pretty limerick ?rst came to my ears in May 1998 during a talk by T.Y. Lam 1 on ?eld invariants from the theory of quadratic forms. It is?poetic exaggeration allowed?a suitable motto for this monograph. What is it about? At the beginning of the seventies I drew up a specialization theoryofquadraticandsymmetricbilinear formsover ?elds[32].Let? : K? L?? be a place. Then one can assign a form? (?)toaform? over K in a meaningful way ? if? has ?good reduction? with respect to? (see§1.1). The basic idea is to simply apply the place? to the coe?cients of?, which must therefore be in the valuation ring of?. The specialization theory of that time was satisfactory as long as the ?eld L, and therefore also K, had characteristic 2. It served me in the ?rst place as the foundation for a theory of generic splitting of quadratic forms [33], [34]. After a very modest beginning, this theory is now in full bloom. It became important for the understanding of quadratic forms over ?elds, as can be seen from the book [26]of Izhboldin?Kahn?Karpenko?Vishik for instance. One should note that there exists a theoryof(partial)genericsplittingofcentralsimplealgebrasandreductivealgebraic groups, parallel to the theory of generic splitting of quadratic forms (see [29] and the literature cited there). PC-PDF, 192 Seiten, XIV Seiten, 192 Seiten, [GR: 9623 - Nonbooks, PBS / Mathematik/Arithmetik, Algebra], [SW: - Algebra ], [Ausgabe: 2010][PU:Springer London]
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ISBN: 9781848822429
ID: 234092
The specialization theory of quadratic and symmetric bilinear forms over fields and the subsequent generic splitting theory of quadratic forms were invented by the author in the mid-1970s. They came to fruition in the ensuing decades and have become an integral part of the geometric methods in quadratic form theory.This book comprehensively covers the specialization and generic splitting theories. These theories, originally developed for fields of characteristic different from 2, are explored here without this restriction.In addition to chapters on specialization theory, generic splitting theory and their applications, the book contains a final chapter containing research never before published on specialization with respect to quadratic places and will provide the reader with a glimpse towards the future.
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Titel: | Specialization of Quadratic and Symmetric Bilinear Forms |
ISBN-Nummer: | 9781848822429 |
Detailangaben zum Buch - Specialization of Quadratic and Symmetric Bilinear Forms
EAN (ISBN-13): 9781848822429
ISBN (ISBN-10): 1848822421
Erscheinungsjahr: 2010
Herausgeber: Springer London
192 Seiten
Sprache: eng/Englisch
Buch in der Datenbank seit 11.06.2012 09:37:36
Buch zuletzt gefunden am 06.09.2016 10:27:29
ISBN/EAN: 9781848822429
ISBN - alternative Schreibweisen:
1-84882-242-1, 978-1-84882-242-9
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