Title of Seminar: Algebraic Geometry Preprint Seminar 2025
Title of Talk: Unirationality and $R$-equivalence for conic bundles over quasi-finite fields.
Speaker: Nidhi Gupta, TIFR, Mumbai
Date: October 7, 2025
Time: 16:00:00 Hours
Venue: AG-77
Abstract: Conic bundle surfaces over $\mathbb{P}^1_k$ are central objects in the birational classification of geometrically rational surfaces over a non-algebraically closed field $k$, and a key open question is whether every conic bundle surface with a $k$-rational point is unirational. This question has been studied over various fields, and in this talk, based on the work of E.~Boughattas (\texttt{arXiv:2410.19686}), we will discuss a partial answer in the case of quasi-finite fields. Specifically, the author shows that over such $k$, a regular conic bundle $X \to \mathbb{P}^1_k$ is unirational if all non-split fibers lie over $k$-rational points. Under the same assumptions, they also show that all $k$-rational points of $X$ are $R$-equivalent.
Title of Talk: Unirationality and $R$-equivalence for conic bundles over quasi-finite fields.
Speaker: Nidhi Gupta, TIFR, Mumbai
Date: October 7, 2025
Time: 16:00:00 Hours
Venue: AG-77
Abstract: Conic bundle surfaces over $\mathbb{P}^1_k$ are central objects in the birational classification of geometrically rational surfaces over a non-algebraically closed field $k$, and a key open question is whether every conic bundle surface with a $k$-rational point is unirational. This question has been studied over various fields, and in this talk, based on the work of E.~Boughattas (\texttt{arXiv:2410.19686}), we will discuss a partial answer in the case of quasi-finite fields. Specifically, the author shows that over such $k$, a regular conic bundle $X \to \mathbb{P}^1_k$ is unirational if all non-split fibers lie over $k$-rational points. Under the same assumptions, they also show that all $k$-rational points of $X$ are $R$-equivalent.