G-torsors and universal torsors over nonsplit del Pezzo surfaces

Autor:	Derenthal, Ulrich, Hoffmann, Norbert
Rok vydání:	2021
Předmět:	Mathematics - Algebraic Geometry Mathematics - Number Theory 14J26 (Primary) 14L30 11E57 14G27 (Secondary)
Druh dokumentu:	Working Paper
Popis:	Let S be a smooth del Pezzo surface that is defined over a field K and splits over a Galois extension L. Let G be either the split reductive group given by the root system of $S_L$ in Pic $S_L$, or a form of it containing the N\'eron-Severi torus. Let $\mathcal{G}$ be the G-torsor over $S_L$ obtained by extension of structure group from a universal torsor $\mathcal{T}$ over $S_L$. We prove that $\mathcal{G}$ does not descend to S unless $\mathcal{T}$ does. This is in contrast to a result of Friedman and Morgan that such $\mathcal{G}$ always descend to singular del Pezzo surfaces over $\mathbb{C}$ from their desingularizations. Comment: 12 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2109.08137 Zobrazit plný text záznamu View this record from Arxiv