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THE MANIN–MUMFORD CONJECTURE: A BRIEF SURVEY

Published online by Cambridge University Press:  21 December 2000

PAVLOS TZERMIAS
PAVLOS TZERMIAS
Affiliation:
Department of Mathematics, P.O. Box 210089, 617 N. Santa Rita, The University of Arizona, Tucson, AZ 85721-0089 USA; e-mail: tzermias@math.arizona.edu
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Abstract

The Manin–Mumford conjecture asserts that if K is a field of characteristic zero, C a smooth proper geometrically irreducible curve over K, and J the Jacobian of C, then for any embedding of C in J, the set C(K) ∩ J(K)tors is finite. Although the conjecture was proved by Raynaud in 1983, and several other proofs have appeared since, a number of natural questions remain open, notably concerning bounds on the size of the intersection and the complete determination of C(K) ∩ J(K)tors for special families of curves C. The first half of this survey paper presents the Manin–Mumford conjecture and related general results, while the second describes recent work mostly dealing with the above questions.

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Type
SURVEY
Information
Bulletin of the London Mathematical Society , Volume 32 , Issue 6 , November 2000 , pp. 641 - 652
Copyright
© The London Mathematical Society 2000

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