This is with reference to theorem 5.20 in Vasconcelos book linked (google books) here: http://tinyurl.com/2967eov
I shall restate the theorem here for easy reference: "If $A=k[[x_1,x_2,...,x_n]]/I$ is a complete intersection and $dim_k A$ is not divisible by $char(k)$ then the Jacobian ideal generates the socle of $A$".
I am looking for a proof of this theorem. Vasconcelos references three places to look for one. One is a result of Tate - I have looked at this. One is supposed to be in Kunz's - Introduction to commutative algebra and algebraic geometry" - I could not find a result similar to this in there (it's not a pointed reference). Finally there is a Scheja-Storch paper linked below. http://www.reference-global.com/doi/abs/10.1515/crll.1975.278-279.174 I am specifically looking for a proof similar to Scheja-Storch (Tate seems to use a different approach), but the above paper is in German and I am not fluent at it. It's probably unlikely, but if anyone has an english reference on this proof, I would really appreciate it.