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Thirty years later. (English) Zbl 1095.12003

Adolphson, Alan (ed.) et al., Geometric aspects of Dwork theory. Vol. I, II. Berlin: Walter de Gruyter (ISBN 3-11-017478-2/hbk). 419-436 (2004).
From the introduction: B. Dwork set up \(p\)-adic differential equation theory thirty years ago in three papers [Bull. Soc. Math. Fr., Suppl., Mém. 39–40, 27–37 (1974; Zbl 0304.14014); Ann. Math. (2) 98, 366–376 (1973; Zbl 0304.14015); Invent. Math. 20, 35–45 (1973; Zbl 0309.14019)]. The few earlier works on this topic were attempts to translate the complex theory and led to poor results. On the basis of his experience with differential equations “coming from geometry”, Dwork introduced three basic notions: – generic points, – the transfer principle, – weak and strong Frobenius structures.
The aim of this paper is to show that these notions were so relevant that they are still useful thirty years later.
For the entire collection see [Zbl 1047.14001].

MSC:

12H25 \(p\)-adic differential equations
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