Download O-Minimality and Diophantine Geometry (London Mathematical by G. O. Jones,A. J. Wilkie PDF

By G. O. Jones,A. J. Wilkie

This number of articles, originating from a brief direction held on the college of Manchester, explores the information in the back of Pila's evidence of the Andre–Oort conjecture for items of modular curves. the elemental approach has 3 major components: the Pila–Wilkie theorem, bounds on Galois orbits, and sensible transcendence effects. All of those subject matters are coated during this quantity, making it excellent for researchers wishing to maintain so far with the most recent advancements within the box. unique papers are mixed with heritage articles in either the quantity theoretic and version theoretic facets of the topic. those comprise Martin Orr's survey of abelian kinds, Christopher Daw's creation to Shimura forms, and Jacob Tsimerman's facts through o-minimality of Ax's theorem at the useful case of Schanuel's conjecture.

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