Title of Seminar: Algebraic Geometry Preprint Seminar 2025
Title of Talk: On the Reconstruction of Schemes from their Etale Topoi
Speaker: Ritankar Nath, TIFR, Mumbai
Date: February 24, 2025
Time: 16:00:00 Hours
Venue: AG-77
Abstract: The etale reconstruction problem asks that given two finite-type schemes $X$ and $Y$ over a field $k$, whether a map between their etale topos comes from an honest map of schemes. This question was first raised by Grothendieck in his 1983 letter to Faltings and subsequently studied by Voevodsky over a finitely generated field of characteristic zero. The talk is based on the preprint https://arxiv.org/abs/2407.19920v1, where the authors discuss this problem over a class of fields called "amenable discretely valued fields". In this talk, we will explore various successes and failures of this problem.
Title of Talk: On the Reconstruction of Schemes from their Etale Topoi
Speaker: Ritankar Nath, TIFR, Mumbai
Date: February 24, 2025
Time: 16:00:00 Hours
Venue: AG-77
Abstract: The etale reconstruction problem asks that given two finite-type schemes $X$ and $Y$ over a field $k$, whether a map between their etale topos comes from an honest map of schemes. This question was first raised by Grothendieck in his 1983 letter to Faltings and subsequently studied by Voevodsky over a finitely generated field of characteristic zero. The talk is based on the preprint https://arxiv.org/abs/2407.19920v1, where the authors discuss this problem over a class of fields called "amenable discretely valued fields". In this talk, we will explore various successes and failures of this problem.