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By Manfred Knebusch

A Mathematician stated Who Can Quote Me a Theorem that’s precise? For those that i do know Are easily now not So, whilst the attribute is 2! this beautiful limerick ?rst got here to my ears in could 1998 in the course of a conversation via T.Y. Lam 1 on ?eld invariants from the idea of quadratic kinds. It is—poetic exaggeration allowed—a compatible motto for this monograph. what's it approximately? initially of the seventies I drew up a specialization theoryofquadraticandsymmetricbilinear formsover ?elds[32].Let? : okay? L?? be a spot. Then one could assign a sort? (?)toaform? over okay in a significant approach ? if? has “good aid” with recognize to? (see§1.1). the elemental suggestion is to easily observe where? to the coe?cients of?, which needs to consequently be within the valuation ring of?. The specialization conception of that point used to be passable so long as the ?eld L, and hence additionally okay, had attribute 2. It served me within the ?rst position because the origin for a thought of widely used splitting of quadratic types [33], [34]. After a really modest starting, this idea is now in complete bloom. It turned vital for the certainty of quadratic kinds over ?elds, as should be obvious from the ebook [26]of Izhboldin–Kahn–Karpenko–Vishik for example. One may still notice that there exists a theoryof(partial)genericsplittingofcentralsimplealgebrasandreductivealgebraic teams, parallel to the speculation of universal splitting of quadratic types (see [29] and the literature mentioned there).

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