User:TakuyaMurata/D-scheme

In algebraic geometry, a $$\mathcal{D}_X$$-scheme is a scheme over a scheme X with flat connection along X. If C is an algebra, it can be equipped with obvious connection, resulting in a $$\mathcal{D}_X$$-algebra $$C_X$$. The functor $$C \mapsto C_X$$ admits a left-adjoint $$H_\nabla(X, –)$$. The functor forgetting $$\mathcal{D}_X$$-structure (trivially) admits a left-adjoint J. If A is a commutative algebra, $$\operatorname{Spec} (JA)$$ is called the scheme of $$\infty$$-jets of sections of $$\operatorname{Spec} A$$.