Abstract
We prove that a local homomorphism induces a flat homomorphism of the graduations with respect to the maximal ideals iff it is flat itself and the tangent cone of the fiber is just the fiber of the tangent cone mapping. More explicit, the statement we want to prove here is as follows.
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References
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Herzog, B. A criterion for tangential flatness. Manuscripta Math 43, 219–228 (1983). https://doi.org/10.1007/BF01165831
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DOI: https://doi.org/10.1007/BF01165831