Bia{\l}ynicki-Birula decomposition for reductive groups

Autor:	Jelisiejew, Joachim, Sienkiewicz, Łukasz
Rok vydání:	2018
Předmět:	Mathematics - Algebraic Geometry Mathematics - Representation Theory 14L30 20G15 (Primary) 14D22 20G05 (Secondary)
Druh dokumentu:	Working Paper
Popis:	We generalize the Bia{\l}ynicki-Birula decomposition from actions of $G_m$ on smooth varieties to actions of linearly reductive group ${\bf G}$ on finite type schemes and algebraic spaces. We also provide a relative version and briefly discuss the case of algebraic stacks. We define the Bia{\l}ynicki-Birula decomposition functorially: for a fixed ${\bf G}$-scheme $X$ and a monoid $\overline{\bf G}$ which partially compactifies ${\bf G}$, the BB decomposition parameterizes ${\bf G}$-schemes over $X$ for which the ${\bf G}$-action extends to the $\overline{\bf G}$-action. The freedom of choice of $\overline{\bf G}$ makes the theory richer than the $G_m$-case. Comment: v3, final. To appear in Journal de Math\'ematiques Pures et Appliqu\'ees
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1805.11558 Zobrazit plný text záznamu View this record from Arxiv