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SUMMARY:On smooth integration of p-nilpotent Lie algebras in positive char
 acteristic
DTSTART:20251211T130000Z
DTEND:20251211T150000Z
DTSTAMP:20260505T203400Z
UID:indico-event-15066@indico.math.cnrs.fr
DESCRIPTION:Speakers: Marion Jeannin\n\nLet k be a field of characteristic
  zero\, and let u be a nilpotent k-Lie algebra of finite dimension. The Ba
 ker–Campbell–Hausdorff formula\, induced by the exponential map\, defi
 nes a group law on the vector group V(u)\, making it into a unipotent alge
 braic k-group. In otherwords\, there is an equivalence between the categor
 y of nilpotent k-Lie algebras of finite dimension and unipotent algebraic 
 k-groups. On the other hand\, the functor G → Lie(G) induces a quasi-inv
 erse equivalence. If now k is of characteristic p > 0\, such a nice conver
 sation between (unipotent algebraic) groups and (nilpotent) Lie algebras n
 o longer exists in general\, but one can still wonder whether under suitab
 le assumptions it is still possible to associate a unipotent algebraic gro
 up to a “nilpotent” (this notion will need to be adapted to the contex
 t) Lie algebra. More precisely\, in this talk we wonder whether\, given a 
 field of positive characteristic k\, a reductive k-group G and a restricte
 d p-nil subalgebra u of the Lie algebra of G\, there existsa smooth unipot
 ent subgroup U ⊂ G such that Lie(U) = u. Obstructions are both arithmeti
 c and algebraic : what will play the role of the exponential here? This wi
 ll lead us to discuss assumptions to ensure the existence of Springer isom
 orphisms\, and more specifically generalisedexponential maps\; but also ge
 ometric: algebraic groups are no longer a priori smooth in positivecharact
 eristic\, a way of controlling the lack of smoothness is to refine the not
 ion of infinitesimalsaturation\, first introduced by Deligne.\n \n\nhttps
 ://indico.math.cnrs.fr/event/15066/
LOCATION:M7-411
URL:https://indico.math.cnrs.fr/event/15066/
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