Grothendieck's specialization homomorphism and and the lifting problem of schemes in positive characteristic

Time: 15:30-16:45, 14-12-2023

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

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Abstract: This talk will first explain Grothendiecks specialization homomorphism of the 'etale fundamental group. References: [SGA1, Expos_e XIII, 2.10]. This map is used to compare fundamental group schemes in zero and positive characteristic and whence derived properties of the _etale fundamental group in positive characteristic. The results obtained can be used to address the lifting problem: what are the obstructions to lifting a scheme in characteristic p to one in characteristic 0. The main reference are Sections 4 and 5 in [Esn23].

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