Titlebook: Local Systems in Algebraic-Arithmetic Geometry; Hélène Esnault Book 2023 The Editor(s) (if applicable) and The Author(s), under exclusive

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exclusice

Hélène Esnault(Over)view on the relation between local systems in complex algebraic geometry and in arithmetic geometry.Discusses deep conjectures that are presently out of reach.Proposes sub-conjectures that might

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Lecture Notes in Mathematicshttp://image.papertrans.cn/l/image/587717.jpg

柔美流畅

https://doi.org/10.1007/978-3-031-40840-3Motives; Local Systems; Hodge Theory; p-adic Hodge Theory; Algebraic Geometry; Complex Local Systems; l-ad

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Lecture 5: Interlude on Some Difference Between the Fundamental Groups in Characteristic 0 and ,See the Abstract of Chap. .: we show here the existence of an obstruction to lift a smooth (quasi-)projective variety defined over an algebraically closed field . of characteristic . to characteristic 0 which relies purely on the shape of its (tame) fundamental group.

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,Lecture 3: Malčev-Grothendieck’s Theorem, Its Variants in Characteristic ,, Gieseker’s Conjecture, lgebraic completion. We recall Grothendieck’s version of it formulated with .-modules using the Riemann-Hilbert correspondence, then the Gieseker conjecture, its counterpart in characteristic ., its solution and generalizations.

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