Finite subgroups of the birational automorphism group are 'almost' nilpotent of class at most two
https://arxiv.org/abs/2004.11715

prikol kstati, gruppa biracionalnyh avtomorphizmov lyubogo mnogoobraziya v char=0
yavlyaetsya 2-nilpotent Jordan, to est' sushchestvuet konstanta K (zavisyashaya ot mnogoobraziya)
tajaya chto lyubaya konechnaya podgruppa soderzhit nilpotentnuyu podgruppu glubinoy ne bol'she 2
i indexa ne bol'she K.

pri etom interesno chto analoga teoremy Prohorova-Shramova (chto lyubaya konechnaya gruppa soderzhit razreshimyu ogranichennogo indexa)
dlya grupp diffeomorfizmov net (a gipoteza est'), Ignasi Mundet i Riera dlya kuchi sluchaev dokazal no ochen' konkretnyh

hotya istoriya voobshe vyglyafit kak paralel'naya. I dazhe est' geometricheskiy analog (po krayney mere filosofskiy) ogranichennosti Fano (BAB) -- teorema kompaktnosti gromova + stabil'nost' perelmana (prostransv s ogranichennoy snizu kriviznoy i ogranichennym snizu ob'emom i sverhu -- diametrom konechnoe chislo tipov diffeomoerfizma)