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DTSTART;TZID=Europe/Paris:20251007T133000
DTEND;TZID=Europe/Paris:20251007T143000
DTSTAMP:20260411T204527
CREATED:20250620T082501Z
LAST-MODIFIED:20251009T114319Z
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SUMMARY:AG : Seda Albayrak (SFU\, Canada) : A refinement of Christol’s theorem for sparse algebraic power series
DESCRIPTION:Abstract: A famous result of Christol gives that a power series \(F(t)=\sum_{n\ge 0} f(n)t^n\) with coefficients in a finite field \(\mathbb{F}_q\) of characteristic \(p\) is algebraic over the field of rational functions in \(t\) if and only if there is a finite-state automaton accepting the base-\(p\) digits of \(n\) as input and giving \(f(n)\) as output for every \(n\ge 0\). An extension of Christol’s theorem\, giving a complete description of the algebraic closure of \(\mathbb{F}_q(t)\)\, was later given by Kedlaya. When one looks at the support of an algebraic power series\, that is the set of \(n\) for which \(f(n)\neq 0\)\, a well-known dichotomy for sets generated by finite-state automata shows that the support set is either sparse—with the number of \(n\le x\) for which \(f(n)\neq 0\) bounded by a polynomial in \(\log(x)\)—or it is reasonably large in the sense that the number of \(n\le x\) with \(f(n)\neq 0\) grows faster than \(x^{\alpha}\) for some positive \(\alpha\). The collection of algebraic power series with sparse supports forms a ring and we give a purely algebraic characterization of this ring in terms of Artin-Schreier extensions and we extend this to the context of Kedlaya’s work on generalized power series. (Joint work with Jason Bell).
URL:https://lmv.math.cnrs.fr/evenenement/ag-seda-albayrak-sfu-canada/
LOCATION:Bâtiment Fermat\, salle 4205
CATEGORIES:Séminaire AG
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DTSTART;TZID=Europe/Paris:20251014T133000
DTEND;TZID=Europe/Paris:20251014T143000
DTSTAMP:20260411T204527
CREATED:20251007T153917Z
LAST-MODIFIED:20251010T080344Z
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SUMMARY:AG : John Lesieutre (Pennsylvania State University) : Volume near the pseudoeffective boundary
DESCRIPTION:Abstract: Suppose that X is a projective variety and that L is a line bundle on X. The volume of L is a measure of the asymptotic growth rate of the number of sections of tensor powers of L. After providing some background on this invariant\, I will explain some pathological behaviors of the volume function which have origins in the dynamics of birational automorphisms of a certain Calabi-Yau threefold X.
URL:https://lmv.math.cnrs.fr/evenenement/ag-john-lesieutre-pennsylvania-state-university/
LOCATION:Bâtiment Fermat\, salle 4205
CATEGORIES:Séminaire AG
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