000			02964nam a22003978i 4500
001			CR9781316106839
003			UkCbUP
005			20200124160214.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			140530s2015||||enk o ||1 0|eng|d
020			_a9781316106839 (ebook)
020			_z9781107462496 (paperback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA242.5 _b.O45 2015
082	0	0	_a516.3/5 _223
245	0	0	_aO-minimality and diophantine geometry / _cedited by G.O. Jones, University of Manchester, A.J. Wilkie, University of Manchester,.
246	3		_aO-Minimality & Diophantine Geometry
264		1	_aCambridge : _bCambridge University Press, _c2015.
300			_a1 online resource (xii, 221 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aLondon Mathematical Society lecture note series ; _v421
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	0	0	_tThe Manin-Mumford Conjecture, an elliptic Curve, its Torsion Points & their Galois Orbits / _rP. Habegger -- _tRational points on definable sets / _rA.J. Wilkie -- _tFunctional transcendence via o-minimality / _rJonathan Pila -- _tIntroduction to abelian varieties and the Ax-Lindemann-Weierstrass theorem / _rMartin Orr -- _tThe André-Oort conjecture via o-minimality / _rChristopher Daw -- _tLectures on elimination theory for semialgebraic and subanalytic sets / _rA.J. Wilkie -- _tRelative Manin-Mumford for abelian varieties / _rD. Masser -- _tImproving the bound in the Pila-Wilkie theorem for curves / _rG.O. Jones -- _tAx-Schanuel and o-minimality / _rJacob Tsimerman.
520			_aThis collection of articles, originating from a short course held at the University of Manchester, explores the ideas behind Pila's proof of the Andre-Oort conjecture for products of modular curves. The basic strategy has three main ingredients: the Pila-Wilkie theorem, bounds on Galois orbits, and functional transcendence results. All of these topics are covered in this volume, making it ideal for researchers wishing to keep up to date with the latest developments in the field. Original papers are combined with background articles in both the number theoretic and model theoretic aspects of the subject. These include Martin Orr's survey of abelian varieties, Christopher Daw's introduction to Shimura varieties, and Jacob Tsimerman's proof via o-minimality of Ax's theorem on the functional case of Schanuel's conjecture.
650		0	_aArithmetical algebraic geometry.
650		0	_aModel theory.
650		0	_aGeometry, Analytic.
700	1		_aJones, G. O. _q(Gareth Owen), _eeditor.
700	1		_aWilkie, A. J. _q(Alec J.), _eeditor.
776	0	8	_iPrint version: _z9781107462496
830		0	_aLondon Mathematical Society lecture note series ; _v421.
856	4	0	_uhttps://doi.org/10.1017/CBO9781316106839
999			_c516136 _d516134