Malcev-Grothendieck theorem and its variants

Time: 14-15:15, 14-12-2023

Venue: Room 612, Building A6, Institute of Mathematics, VAST

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Abstract: This talk starts with the Malcev-Grothendieck theorem (over $mathbb{C}$) which roughly says that the 'etale fundamental group controls the number of local systems of fixed rank. We also have its characteristic $p$ version: Gieseker's conjecture, which was proved by Esnault-Mehta. In the case of smooth projective schemes over perfect field of positive characteristic, a variant of Malcev-Grothendieck theorem for the crystalline fundamental groups was conjectured by de Jong. References[Esn23, 3.3 and 3.4] and references therein, especially [EM10, ES18].
 

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