Derived & Noncommutative Geometry: A derived dreamwalk toward p-curvature

Speaker: Jiaqi Fu (University of Toulouse)

Time: 2026-03-16 15:00-18:30
Location: 1010, SIMIS
Zoom meeting ID: 860 3552 7679 Password: SIMIS

Abstract:

When is a Lie algebra(-oid) in char p>0 integrable? p-Curvature provides a first obstruction in ordinary algebraic geometry. To answer this question in a derived setting, Brantner–Mathew introduced the notion of partition Lie algebras(-oids) to generalize Lurie–Pridham’s theorem to char p>0. Meanwhile, we can still consider the naive derived category of ordinary Lie or p-restricted Lie algebras. In fact there is a reasonable sequence of derived monads
\[\mathrm{Lie}_{\Delta,\bF_p}\to  \mathrm{Lie}^{res}_{\Delta,\bF_p}\to \mathrm{Lie}^{\pi}_{\Delta,\bF_p}.\]
The computation result of me and Nuiten hinted that there exists a derived obstruction theory for the existence of partition Lie structure, that is, obstruction to being formally integrable in char p>0 and in derived setting.