Notes on modules, I

Notes on Equivariant D-modules

Notes on Modules and Algebras

For objects A and B belonging to a category C we denote by C(A,B) the set of all morphisms from A to B in C and, for any f ∈ C(A,B), the objects A and B are called, respectively, the domain and codomain of f . For example, if A and B are abelian groups, and we denote by U(A) and U(B) the underlying sets of A and B, then Ab(A,B) is the set of all group homomorphisms having domain A and codomain ...

Notes on Crystals and Algebraic D-modules

∇ : V → V ⊗ ΩX . Then the flat sections of V determine a local system L on X. For every point x ∈ X, the fiber of the local system Lx can be identified with the fiber Vx. Given a path p : [0, 1] from x = p(0) to y = p(1), there is a map p! : Lx → Ly is given by parallel transport along p, using the connection ∇; moreover the map p! depends only on the homotopy class of the path p. This construc...

on direct sums of baer modules

the notion of baer modules was defined recently

Notes on Sandflies. Part I