Hello, 


Could you help me with a reference to elementary properties of Groebner bases in rings of formal power series over a field? I am especially interested in generic initial ideals.


Thank you in advance,  

Serge



Groebner bases for power series rings (reference request)
To expand on Michael's comment, the Greuel, Pfister book Section 6.4 is about standard bases in formal power series rings. Quoting,



> 
> The main result is that they can be computed, if the ideal is
>  generated by polynomials. This is the basis for computations in local analytic
>  geometry. The theory of standard bases in power series rings goes back to
>  Hironaka (cf. [123]) and Grauert (cf. [98]).
> 
> 
> 


The references are:


* Hironaka, H.: Resolution of Singularities of an Algebraic Variety over a Field
of Characteristic Zero. Ann. of Math. 79, 109–326 (1964).
* Grauert, H.: Über die Deformation isolierter Singularitäten analytischer Mengen. Invent. Math. 15, 171–198 (1972).


