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{\Large המחלקה למתמטיקה, בן-גוריון}

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{\Huge גאומטריה אלגברית ותורת המספרים}\\[0.2\baselineskip]

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\textbf{ב}\emph{יום שלישי, 16 ביוני, 2015}
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\textbf{בשעה} \emph{10:00 -- 11:00}
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\textbf{ב}\emph{Math -101}

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ההרצאה

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{\Large\bfseries Stability of Gauss valuations\par}
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תינתן על-ידי
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{\large\scshape Antoine Ducros 
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  (Paris 6)
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\textbf{תקציר:}
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A valued field (k, & . & ) is said to be stable (this terminology has no link with model-theoretic stability theory) if every finite extension L of k is defectless, /i.e. /satisfies the equality ∑ e\_vf\_v= {[}L:k{]} where v goes through the set of extensions of & . & to L, and where e\_v and f\_v are the ramification and inertia indexes of v. The purpose of my talk is to present a new proof (which is part of current joint reflexions with E. Hrushovski and F. Loeser) of the following classical fact (Grauert, Kuhlmann, Temkin\ldots{}) : let (k, & . & ) be a stable valued field, and let (r\_1,\ldots{},r\_n) be elements of an ordered abelian group G containing & k\^{}* & . Let & . & ` be the G-valued valuation on k(T\_1,\ldots{},T\_n) that sends ∑ a\_I T\^{}I to max & a\_I & .r\^{}I. Then (k(T\_1,\ldots{},T\_n), & . & `) is stable too. Our general strategy is purely geometric, but the proof is based upon model-theoretic tools coming from model theory (which I will first present; no knowledge of model theory will be assumed). In particular, it uses in a crucial way a geometric object defined in model-theoretic terms that Hrushovski and Loeser attach to a given k-variety X, which is called its /stable completion/; the only case we will have to consider is that of a curve, in which the stable completion has a very nice model-theoretic property, namely the definability, which makes it very easy to work with.\\
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{\bfseries אנא שימו לב לשינוי ביום ושעה!}
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