Considering f:XtomathbbCf:XtomathbbC, g:XtomathbbC and foplusg:(x,y)mapstof(x)+g(y).
The Sebastiani-Thom isomorphism is an isomorphism Phifoplusg(MboxtimesN)=Phif(M)otimesPhig(N) compatible with monodromies.
The original theorem was for constant coefficient M=mathbbCX, N=mathbbCY. 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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