, Volume 43, Issue 2-3, pp 219-228

A criterion for tangential flatness

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


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.