Mathematics

We will discuss chapter 4 of Toen's notes. In particular we will discuss the simplicial analogues of rings (i.e., affine schemes) and modules (i.e. quasicoherent shaves on them), that is the simplicial model category sComm of simplicial algebras and, for a given simplicial algebra A, that of its simplicial modules sA-Mod. Of particular interest is the simplicial analogue of the Kaehler differentials/cotangent sheaf, the oldest example of derived geometry appearing in classical algebraic geometry.