V. Srinivas
SUNY Buffalo
January 9, 2025
Etale fundamental groups in characteristic p: For a variety over an algebraically closed field of characteristic 0, the etale fundamental group, defined by Grothendieck, reflects properties of the topological fundamental group. For varieties over fields of characteristic p, some aspects do reflect properties which we may think of as related to ``topology'', particularly in situations where the variety is obtained by ``reduction mod p'' from a variety in characteristic 0, while other aspects do not readily have such an interpretation. I will give an introduction to this topic, and then focus on some recent results obtained in work with Esnault and other collaborators.
SUNY Buffalo
January 9, 2025
Etale fundamental groups in characteristic p: For a variety over an algebraically closed field of characteristic 0, the etale fundamental group, defined by Grothendieck, reflects properties of the topological fundamental group. For varieties over fields of characteristic p, some aspects do reflect properties which we may think of as related to ``topology'', particularly in situations where the variety is obtained by ``reduction mod p'' from a variety in characteristic 0, while other aspects do not readily have such an interpretation. I will give an introduction to this topic, and then focus on some recent results obtained in work with Esnault and other collaborators.