Addendum to the text of W. D. Brownawell: “Bounds for the degrees in the Nullstellensatz”. (A propos du texte de W. D. Brownawell: “Bounds for the degrees in the Nullstellensatz”.) (French) Zbl 0641.14002

Philippon, Patrice

Ann. Math. (2) 127, No. 2, 367-371 (1988).

In the paper which is mentioned in the title, W. D. Brownawell [ibid. 126, 577–591 (1987; Zbl 0641.14001)] proved a remarkable result which is the first sharp effective version of Hilbert’s Nullstellensatz. His main proposition uses elimination theory, and his final result combines this proposition with a result from complex analysis due to Skoda.
In the present note, the author shows that his previous paper [Publ. Math., Inst. Hautes Étud. Sci. 64, 5–52 (1986; Zbl 0615.10044)] enables him to get an explicit version of Brownawell’s main proposition for algebraic number fields.

Reviewer: Michel Waldschmidt (Paris)

MSC:

14A05	Relevant commutative algebra
11R09	Polynomials (irreducibility, etc.)
13F20	Polynomial rings and ideals; rings of integer-valued polynomials
11C08	Polynomials in number theory

Keywords:

effectivity; effective version of Hilbert’s Nullstellensatz; elimination

Citations:

Zbl 0641.14001; Zbl 0615.10044