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Let $P$ be an analytic linear differential operator defined on some open interval $X=(a,b)$ and $\mathcal{M}=\mathcal{D}_X / \mathcal{D}_X \bullet P$ the corresponding $\mathcal{D}$-module. I'm trying …

Let $V \in C^{1}(\mathbb{R}^n, \mathbb{R})$ consider the following PDE: $$u_t = grad[V(u)]$$ For $u \in C^{1}([0,1]^n\times [0,T),\mathbb{R}^n)$, with boundary conditions specified on the $n$-dimens …

Let $\mathfrak{gl}_n(x)= \mathfrak{gl}_n \otimes_\mathbb{C}\mathbb{C}(x)$ be the algebra of matrices taking values in rational functions. Definition: Two matrices $A, B \in \mathfrak{gl}_n(x)$ ar …

I will assume $G \subset SO(3)$ (I m not sure yet about the general case). By the following answer we know $SO(3,\mathbb{C})$ has double cover $SL(2,\mathbb{C})$ (which is simply connected). All fini …

Let $X$ be a smooth curve over an algebraically closed field of characteristic 0. The category of quasi-coherent $D$-modules $\mathcal{D}_X$-$Mod$ is a symmetric monoidal abelian category. We can ther …

Let $k$ be an algebraically closed field of characteristic 0. Consider the field of fractions of formal power series $K:= Frac(k[[T_1,...,T_n]])$. We have the corresponding algebra of differential ope …

Disclaimer: I know very little about both of the fields in question. My question is pretty simple: What's the relation between differential Galois theory and D-modules over algebraic curves? …

Main Question: What Is the correpondence between flows and vector fields in algebraic geometry? Here is a more precise statement could be an answer If it was true (I have no idea it is): "P …