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Le probl\`eme de la sch\'ematisation de Grothendieck revisit\'e

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arxiv 1911.05509 v3 pith:SOS3TE3E submitted 2019-11-13 math.AG math.AT

classification math.AGmath.AT
keywords schematizationhomotopyproblembehaviourcaseconjconjectureconnected
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The objective of this work is to reconsider the schematization problem of [6], with a particular focus on the global case over Z. For this, we prove the conjecture [Conj. 2.3.6][15] which gives a formula for the homotopy groups of the schematization of a simply connected homotopy type. We deduce from this several results on the behaviour of the schematization functor, which we propose as a solution to the schematization problem.

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