caa a22 4500 606244689 CHVBK 20210128101331.0 cr unu---uuuuu 210128e20150501xx s 000 0 eng 10.1007/s12044-015-0234-7 doi (NATIONALLICENCE)springer-10.1007/s12044-015-0234-7 MARGAUX BENEDICTUS Laboratoire de Recherche "Princess Stephanie”, 51840, Monte Carlo, Monaco aut Smoothness of limit functors [Elektronische Daten] [BENEDICTUS MARGAUX] Let S be a scheme. Assume that we are given an action of the one dimensional split torus G m , S $\mathbb {G}_{m,S}$ on a smooth affine S-scheme X $\mathfrak {X}$ . We consider the limit (also called attractor) subfunctor X λ $\mathfrak {X}_{\lambda }$ consisting of points whose orbit under the given action ‘admits a limit at 0'. We show that X λ $\mathfrak {X}_{\lambda }$ is representable by a smooth closed subscheme of X $\mathfrak {X}$ . This result generalizes a theorem of Conrad et al. (Pseudo-reductive groups (2010) Cambridge Univ. Press) where the case when X $\mathfrak {X}$ is an affine smooth group and G m , S $\mathbb {G}_{m,S}$ acts as a group automorphisms of X $\mathfrak {X}$ is considered. It also occurs as a special case of a recent result by Drinfeld on the action of G m , S $\mathbb {G}_{m,S}$ on algebraic spaces (Proposition 1.4.20 of Drinfeld V, On algebraic spaces with an action of G m $\mathfrak {G}_{m}$ , preprint 2013) in case S is of finite type over a field. Indian Academy of Sciences, 2015 Group schemes nationallicence torus action nationallicence limit subscheme nationallicence Proceedings - Mathematical Sciences Springer India 125/2(2015-05-01), 161-165 0253-4142 125:2<161 2015 125 12044 https://doi.org/10.1007/s12044-015-0234-7 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s12044-015-0234-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- MARGAUX BENEDICTUS Laboratoire de Recherche "Princess Stephanie”, 51840, Monte Carlo, Monaco aut NATIONALLICENCE 773 0- Proceedings - Mathematical Sciences Springer India 125/2(2015-05-01), 161-165 0253-4142 125:2<161 2015 125 12044