{"id":"hexagon/2610.00030","pdf":"https://hexagonmath.org/pdf/2610.00030v1","url":"https://hexagonmath.org/abs/2610.00030v1","tags":["math.AT","math.SG","msc:14F40","Derived algebraic geometry","deformation theory","derived algebra","infinity-categories","shifted Poisson structures","shifted symplectic structures"],"score":0,"title":"Crystalline and infinitesimal Poisson stacks","domain":"math.AG","source":"hexagon","authors":["Aleksandr Karapetyan"],"reviews":0,"subject":"math.AG","summary":"A systematic way to construct Poisson brackets on moduli stacks in algebraic geometry is through shifted Poisson structures on derived stacks. The standard construction, due to Calaque--Pantev--To{\\\"e}n--Vaqui{\\'e}--Vezzosi, imports Gelfand--Kazhdan formal geometry to derived stacks in order to establish formal descent for polyvector fields. The result is a graded Lie algebra which we call the ``crystalline'' polyvector fields on a derived stack. Using instead the formal derived geometry machinery of Gaitsgory--Rozenblyum, we construct a graded Lie algebra of ``infinitesimal'' polyvector…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-04","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}