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X-WR-CALDESC:évènements pour Département de mathématiques et applications
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DTSTART:20180325T010000
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DTSTART:20181028T010000
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DTSTART;TZID=Europe/Paris:20180323T110000
DTEND;TZID=Europe/Paris:20180323T110000
DTSTAMP:20260408T155018
CREATED:20180323T100000Z
LAST-MODIFIED:20211104T110539Z
UID:8454-1521802800-1521802800@www.math.ens.psl.eu
SUMMARY:On a conjecture of Colliot-Thélène
DESCRIPTION:Let f be a morphism of projective smooth varieties X\, Y defined over the rationals. The conjecture by Colliot-Thélène under discussion gives (conjectural) sufficient conditions which imply that for almost all rational prime numbers p\, the map f maps the p-adic points X(Q_p) surjectively onto Y(Q_p). The aim of the talk is to present some recent results by Denef\, Skorobogatov et al
URL:https://www.math.ens.psl.eu/evenement/on-a-conjecture-of-colliot-thelene/
LOCATION:IHP amphitheatre Darboux
CATEGORIES:Séminaire Géométrie et théorie des modèles
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20180323T141500
DTEND;TZID=Europe/Paris:20180323T154500
DTSTAMP:20260408T155018
CREATED:20180323T131500Z
LAST-MODIFIED:20211104T110538Z
UID:8453-1521814500-1521819900@www.math.ens.psl.eu
SUMMARY:The dynamical Mordell-Lang problem in positive characteristic
DESCRIPTION:The dynamical Mordell-Lang conjecture in characteristic zero predicts that if f : X –> X is a map of algebraic varieties over a field K of characteristic zero\, Y subset X is a closed subvariety and a in X(K) is a K-rational point on X\, then the return set { n in N : f^n(a) in Y(K) } is a finite union of points and arithmetic progressions. For K a field of characteristic p > 0\, it is necessary to allow for finite unions with sets of the form { a + sum_{i=1}^m p^{n_i} : (n_1\, … \, n_m) in N^m } and one might conjecture that all return sets are finite unions of points\, arithmetic progressions and such p-sets. We studied the special case of the positive characteristic dynamical Mordell-Lang problem on semiabelian varieites and using our earlier results with Moosa on so-called F-sets reduced the problem to that of solving a class of exponential diophantine equations in characteristic zero. In so doing\, under the hypothesis that X is a semiabelian variety and either Y has small dimension or f is sufficiently general\, we prove the conjecture. However\, we also show that our reduction to the exponential diiophantine problems may be reversed so that the positive characteristic dynamical Mordell-Lang conjecture in general is equivalent to a class of hard exponential diophantine problems which the experts consider to be out of reach given our present techniques. (This is a report on joint work with Pietro Corvaja\, Dragos Ghioca and Umberto Zannier available at arXiv:1802.05309.)
URL:https://www.math.ens.psl.eu/evenement/the-dynamical-mordell-lang-problem-in-positive-characteristic/
LOCATION:IHP amphitheatre Darboux
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20180323T160000
DTEND;TZID=Europe/Paris:20180323T173000
DTSTAMP:20260408T155018
CREATED:20180323T150000Z
LAST-MODIFIED:20211104T110539Z
UID:8455-1521820800-1521826200@www.math.ens.psl.eu
SUMMARY:A model theoretic generalization of the one-dimensional case of the Elekes-Szabo theorem
DESCRIPTION:(Joint work with A. Chernikov)Let V subseteq C^3 be a complex variety of dimension 2.The Elekes-Szabo Theorem says that if V contains `too many’ points on n x n x n Cartesian products then V has a special form: either V contains a cylinder over a curve or V is related to the graph of the multiplication of an algebraic group.In this talk we generalize the Elekes-Szabo Theorem to relations on strongly minimal sets interpretable in distal structures.
URL:https://www.math.ens.psl.eu/evenement/a-model-theoretic-generalization-of-the-one-dimensional-case-of-the-elekes-szabo-theorem/
LOCATION:IHP amphitheatre Darboux
CATEGORIES:Séminaire Géométrie et théorie des modèles
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