Considering $f:Xto mathbb{C}$, $g:Xto mathbb{C}$ and $foplus g:(x,y)mapsto f(x)+g(y)$.
The Sebastiani-Thom isomorphism is an isomorphism $Phi_{foplus g}(Mboxtimes N) = Phi_{f}(M) otimes Phi_{g}(N)$ compatible with monodromies.
The original theorem was for constant coefficient $M = mathbb{C}_X$, $N = mathbb{C}_Y$. David Massey gave a proof for general constructible coefficients.
Is there an algebraic proof for D-modules?
All proofs use topological arguments that don't seem to translate. In his article "On microlocal b-funtions" Saito mentions a result to be published but I couldn't find it.
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