4053580Specialization of Quadratic and Symmetric Bilinear Formshttps://www.gandhi.com.mx/specialization-of-quadratic-and-symmetric-bilinear-forms-9781848822429/phttps://gandhi.vtexassets.com/arquivos/ids/2561090/23790e59-a38c-4efb-8069-00e108d8519d.jpg?v=6383841420066300009621069MXNSpringer LondonInStock/Ebooks/<p>A Mathematician Said Who Can Quote Me a Theorem thats 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 ispoetic exaggeration alloweda 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? (see1.1). 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 IzhboldinKahnKarpenkoVishik 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).</p>...3989497Specialization of Quadratic and Symmetric Bilinear Forms9621069https://www.gandhi.com.mx/specialization-of-quadratic-and-symmetric-bilinear-forms-9781848822429/phttps://gandhi.vtexassets.com/arquivos/ids/2561090/23790e59-a38c-4efb-8069-00e108d8519d.jpg?v=638384142006630000InStockMXN99999DIEbook20119781848822429_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9781848822429_<p>A Mathematician Said Who Can Quote Me a Theorem thats 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 ispoetic exaggeration alloweda suitable motto for this monograph. What is it about? At the beginning of the seventies I drew up a specialization theoryofquadraticandsymmetricbilinear formsover ?elds32.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? (see1.1). 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 26of IzhboldinKahnKarpenkoVishik 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).</p>9781848822429_Springer Londonlibro_electonico_f53d220d-4c31-3512-bcbb-1df8616bb720_9781848822429;9781848822429_9781848822429Manfred KnebuschInglésMéxico2011-01-22T00:00:00+00:00Springer London