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Une vive querelle oppose en 1874 Camille Jordan et Leopold Kronecker sur l’organisation de la théorie des formes bilinéaires, considérée comme permettant un traitement « général » et « homogène » de nombreuses questions développées dans des cadres théoriques variés au xixe siècle et dont le problème principal est reconnu comme susceptible d’être résolu par deux théorèmes énoncés indépendamment par Jordan et Weierstrass. Cette controverse, suscitée par la rencontre de deux théorèmes que nous considérerions...
Let be a 2-dimensional normal excellent henselian local domain in which is invertible and let and be its fraction field and residue field respectively. Let be the set of rank 1 discrete valuations of corresponding to codimension 1 points of regular proper models of . We prove that a quadratic form over satisfies the local-global principle with respect to in the following two cases: (1) has rank 3 or 4; (2) has rank and , where is a complete discrete valuation ring with...
We examine the conditions for two algebraic function fields over global fields to be Witt equivalent. We develop a criterion solving the problem which is analogous to the local-global principle for Witt equivalence of global fields obtained by R. Perlis, K. Szymiczek, P. E. Conner and R. Litherland [12]. Subsequently, we derive some immediate consequences of this result. In particular we show that Witt equivalence of algebraic function fields (that have rational places) over global fields implies...
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