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Jets via Hasse-Schmidt derivations. (English) Zbl 1194.13027

Zannier, Umberto (ed.), Diophantine geometry. Selected papers of a the workshop, Pisa, Italy, April 12–July 22, 2005. Pisa: Edizioni della Normale (ISBN 978-88-7642-206-5/pbk). Centro di Ricerca Matematica Ennio De Giorgi (CRM) Series (Nuova Serie) 4, 335-361 (2007).
From the text: This paper contains a few brief notes on how to define jets using Hasse-Schmidt higher derivations.
Most of this note consists of straightforward generalizations of the theory of derivations of order 1 as found in A. Grothendieck’s EGA [Publ. Math., Inst. Hautes √Čtud. Sci. 4, 1–228 (1960); ibid. 8, 1–222 (1961); ibid. 11, 349–511 (1962; Zbl 0118.36206); ibid. 17, 137–223 (1963; Zbl 0122.16102); ibid. 20 (1964; Zbl 0136.15901); ibid. 24 (1965; Zbl 0135.39701); ibid. 28 (1966; Zbl 0144.19904); ibid. 32, 361 (1967; Zbl 0153.22301)] or H. Matsumura [“Commutative ring theory” (Cambridge 1986; Zbl 0603.13001)].
For the entire collection see [Zbl 1113.11003].

MSC:

13N15 Derivations and commutative rings
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