منابع مشابه
Rationally isotropic quadratic spaces are locally isotropic
Let R be a regular local ring, K its field of fractions and (V, φ) a quadratic space over R. In the case of R containing a field of characteristic zero we show that if (V, φ)⊗R K is isotropic over K, then (V, φ) is isotropic over R. 1 Characteristic zero case 1.0.1 Theorem (Main). Let R be a regular local ring, K its field of fractions and (V, φ) a quadratic space over R. Suppose R contains a f...
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Acknowledgements I owe a great dept of gratitude to my supervisor Spiros Cotsakis for his encouragement and enthusiasm that were the driving force for starting and completing my PhD. I am also grateful to him for his contribution and guidance in research and in the writing up of our work. This thesis has been influenced dramatically both in style and content from his comments and suggestions. I...
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متن کاملRationally Isotropic Quadratic Spaces Are Locally Isotropic: II
The results of the present article extend the results of [Pa]. The main result of the article is Theorem 1.1 below. The proof is based on a moving lemma from [LM], a recent improvement due to O. Gabber of de Jong’s alteration theorem, and the main theorem of [PR]. A purity theorem for quadratic spaces is proved as well in the same generality as Theorem 1.1, provided that R is local. It generali...
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ژورنال
عنوان ژورنال: Physical Review D
سال: 2004
ISSN: 1550-7998,1550-2368
DOI: 10.1103/physrevd.69.101303