余模范畴中的余倾斜预包络和余倾斜挠类

众所周知, Assem-Smal定理在倾斜理论中有重要的作用.本文的目的是建立一个在余模范畴中的Assem-Smal定理的版本,并通过利用预包络理论来刻画余模范畴中的余倾斜挠类.

Cotilting Preenvelope and Cotilting Torsion Classes in Comodule Categories

The mean-field game is studied for state-affine systems with degenerate state- and distribution-dependent noises. The mean field terms of both drift and diffusion coefficients are allowed to grow in the distribution in a linear way, and therefore the linear-quadratic case (where the expected state appears in a linear way in the system dynamics) is included. The authors prove existence of the solution to the associated forward-backward stochastic differential equations of a McKean-Vlasov type and regularity of the decoupled function. Finally, they prove that solutions of the mean-field game together with the decoupled function approximate the Nash equilibrium of the N-players'' game with an order up to N^{-{1over d+4}}.