Book Review

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MathSciNet review: 3020832

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Book Information:

Author: Umberto Zannier

Title: Some problems of unlikely intersections in arithmetic and geometry

Additional book information: Annals of Mathematics Studies, 181, Princeton University Press, Princeton, New Jersey, 2012, xiv+160 pp., ISBN 978-0-691-15371-1, US $75.00

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**990016**, DOI 10.1007/978-3-663-14108-2

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**505**(1998), 203–208 (French, with English summary). MR

**1662256**, DOI 10.1515/crll.1998.118

*Preperiodic points and unlikely intersections*, Duke Math. J.

**159**(2011), no. 1, 1–29. MR

**2817647**, DOI 10.1215/00127094-1384773

*Anomalous subvarieties—structure theorems and applications*, Int. Math. Res. Not. IMRN

**19**(2007), Art. ID rnm057, 33. MR

**2359537**, DOI 10.1093/imrn/rnm057

*Rational points of a class of algebraic curves*, Izv. Akad. Nauk SSSR Ser. Mat.

**30**(1966), 1373–1396 (Russian). MR

**0205991**

*Intersecting subvarieties of abelian varieties with algebraic subgroups of complementary dimension*, Invent. Math.

**176**(2009), no. 2, 405–447. MR

**2495768**, DOI 10.1007/s00222-008-0170-6

*On the bounded height conjecture*, Int. Math. Res. Not. IMRN

**5**(2009), 860–886. MR

**2482128**, DOI 10.1093/imrn/rnn149

*The $p$-torsion of elliptic curves is uniformly bounded*, Izv. Akad. Nauk SSSR Ser. Mat.

**33**(1969), 459–465 (Russian). MR

**0272786**

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**132**(2010), no. 6, 1677–1691. MR

**2766181**

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**311**(1989), no. 1, 413–424. MR

**974783**, DOI 10.1090/S0002-9947-1989-0974783-6

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**341**(2008), no. 4, 789–824 (French, with English summary). MR

**2407327**, DOI 10.1007/s00208-008-0212-9

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**1472499**

*O-minimality and the André-Oort conjecture for $\Bbb C^n$*, Ann. of Math. (2)

**173**(2011), no. 3, 1779–1840. MR

**2800724**, DOI 10.4007/annals.2011.173.3.11

*Heights and the specialization map for families of abelian varieties*, J. Reine Angew. Math.

**342**(1983), 197–211. MR

**703488**, DOI 10.1515/crll.1983.342.197

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**65**(2002), no. 1, 27–44. MR

**1875133**, DOI 10.1112/S0024610701002861

Review Information:

Reviewer: Joseph H. Silverman

Affiliation: Mathematics Department, Brown University, Providence, Rhode Island 02912

Journal: Bull. Amer. Math. Soc.

**50**(2013), 353-358

DOI: https://doi.org/10.1090/S0273-0979-2012-01386-1

Keywords: unlikely intersection

Published electronically: July 24, 2012

Review copyright: © Copyright 2012 American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.