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Counting special points: logic, Diophantine geometry, and transcendence theory. (English) Zbl 1323.11041
Summary: We expose a theorem of J. Pila [Ann. Math. (2) 173, No. 3, 1779–1840 (2011; Zbl 1243.14022)] and A. J. Wilkie [J. Am. Math. Soc. 9, No. 4, 1051–1094 (1996; Zbl 0892.03013)] on counting rational points in sets definable in o-minimal structures and some applications of this theorem to problems in Diophantine geometry due to Masser, Peterzil, Pila, Starchenko, and Zannier.

MSC:
11G15 Complex multiplication and moduli of abelian varieties
03C64 Model theory of ordered structures; o-minimality
11J81 Transcendence (general theory)
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