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Titlebook: Specialization of Quadratic and Symmetric Bilinear Forms; Manfred Knebusch Book 2010 Springer-Verlag London Limited 2010 DEX.Generic split

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书目名称Specialization of Quadratic and Symmetric Bilinear Forms
编辑Manfred Knebusch
视频video
概述Written by the founder of specialization theory of quadratic and symmetric bilinear forms over fields and the subsequent generic splitting theory of quadratic forms.Comprehensively covers specializati
丛书名称Algebra and Applications
图书封面Titlebook: Specialization of Quadratic and Symmetric Bilinear Forms;  Manfred Knebusch Book 2010 Springer-Verlag London Limited 2010 DEX.Generic split
描述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 insta
出版日期Book 2010
关键词DEX; Generic splitting theory; Quadratic forms; Specialization theory; Symmetric bilinear forms; addition
版次1
doihttps://doi.org/10.1007/978-1-84882-242-9
isbn_softcover978-1-4471-2586-0
isbn_ebook978-1-84882-242-9Series ISSN 1572-5553 Series E-ISSN 2192-2950
issn_series 1572-5553
copyrightSpringer-Verlag London Limited 2010
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https://doi.org/10.1007/978-1-84882-242-9DEX; Generic splitting theory; Quadratic forms; Specialization theory; Symmetric bilinear forms; addition
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Generic Splitting Theory,ic point of view was to bring quadratic and bilinear modules over valuation rings into the game. For our specialization theory, these modules were merely an aid however, and their rôle has now more or less ended.
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Some Applications,The theory of weak specialization, developed in §1.3, §1.7 and the end of §2.3, has until now played only an auxiliary role, which we could have done without when dealing with quadratic forms (due to Theorem 2.19). For the first time we now come to independent applications of weak specialization.
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Manfred KnebuschWritten by the founder of specialization theory of quadratic and symmetric bilinear forms over fields and the subsequent generic splitting theory of quadratic forms.Comprehensively covers specializati
发表于 2025-3-23 02:49:12 | 显示全部楼层
Specialization with Respect to Quadratic Places, ..(.) = dim .. The form ..(.) is only determined up to stable isometry by the form ., however. In truth we thus associated to . only a stable isometry class of forms over .. Nonetheless we will disregard this fact and just speak of ..(.) as if it were a form over ..
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1572-5553 heory of quadratic forms.Comprehensively covers specializatiA 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 fr
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