Title of Seminar: Algebraic Geometry Preprint Seminar
Title of Talk: On the Grothendieck Serre Conjecture for smooth schemes over Prufer bases
Speaker: Ritankar Nath, TIFR, Mumbai
Date: February 6, 2024
Time: 16:00:00 Hours
Venue: AG-77
Abstract: The Grothendieck-Serre Conjecture tells us that given a regular local ring $R$ and a reductive $R$-group scheme $G$, every non-trivial $G$-torsor on $R$ remains non-trivial over its fraction field. In the talk, several known cases of the Grothendieck-Serre conjecture will be discussed, particularly its analogue when $R$ is a semilocal Prufer domain. Then, we will explicitly prove the conjecture for some cases when $R$ is the localisation at finitely many points of a smooth scheme over a semilocal Prufer domain. We will mainly follow the preprint https://arxiv.org/abs/2301.12460 titled "Grothendieck-Serre for constant reductive group schemes" by Ning Guo and Fei Liu.
Title of Talk: On the Grothendieck Serre Conjecture for smooth schemes over Prufer bases
Speaker: Ritankar Nath, TIFR, Mumbai
Date: February 6, 2024
Time: 16:00:00 Hours
Venue: AG-77
Abstract: The Grothendieck-Serre Conjecture tells us that given a regular local ring $R$ and a reductive $R$-group scheme $G$, every non-trivial $G$-torsor on $R$ remains non-trivial over its fraction field. In the talk, several known cases of the Grothendieck-Serre conjecture will be discussed, particularly its analogue when $R$ is a semilocal Prufer domain. Then, we will explicitly prove the conjecture for some cases when $R$ is the localisation at finitely many points of a smooth scheme over a semilocal Prufer domain. We will mainly follow the preprint https://arxiv.org/abs/2301.12460 titled "Grothendieck-Serre for constant reductive group schemes" by Ning Guo and Fei Liu.