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Lukas Brantner: Lie algebras, Galois theory, and deformations of Calabi–Yau varieties

Time: Thu 2022-03-24 14.15 - 16.00

Location: Institut Mittag-Leffler, Seminar Hall Kuskvillan and Zoom

Video link: Meeting ID: 921 756 1880

Participating: Lukas Brantner (Oxford University / Université Paris-Saclay)

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We give an overview of some recent developments in algebraic geometry in characteristic p. First, we introduce a good substitute of dg Lie algebras in this setting, which leads to a classification of formal moduli problems. Next, we use these new Lie algebras to construct a Galois correspondence for purely inseparable field extensions, generalising a result of Jacobson at height one. Finally, we prove that ordinary Calabi–Yau varieties in characteristic p are unobstructed and admit canonical lifts, generalising results of Serre–Tate, Deligne–Nygaard, Ward, and Achinger–Zdanowic. This talk is based on separate joint works with Mathew, Taelman, and Waldron.