For other uniform boundedness conjectures, see Uniform boundedness conjecture.
In algebraic geometry and number theory, the torsion conjecture or uniform boundedness conjecture for torsion points for abelian varieties states that the order of the torsion group of an abelian variety over a number field can be bounded in terms of the dimension of the variety and the number field. A stronger version of the conjecture is that the torsion is bounded in terms of the dimension of the variety and the degree of the number field. The torsion conjecture has been completely resolved in the case of elliptic curves.
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theory, the torsionconjecture or uniform boundedness conjecture for torsion points for abelian varieties states that the order of the torsion group of an...
for testing conjectures. In papers in 1977 and 1978, Barry Mazur proved the torsionconjecture giving a complete list of the possible torsion subgroups...
The simplest adjustment of the integral Hodge conjecture is: Integral Hodge conjecture modulo torsion. Let X be a projective complex manifold. Then every...
Tietze. This conjecture is now known to be false. The non-manifold version was disproved by John Milnor in 1961 using Reidemeister torsion. The manifold...
Neumann conjecture stated that a group G is non-amenable if and only if G contains a subgroup that is a free group on two generators. The conjecture was disproved...
The abc conjecture (also known as the Oesterlé–Masser conjecture) is a conjecture in number theory that arose out of a discussion of Joseph Oesterlé and...
Uniform boundedness conjecture may refer to: Uniform boundedness conjecture for torsion points Uniform boundedness conjecture for rational points Uniform...
Reidemeister torsion. Jeff Cheeger (1977, 1979) and Werner Müller (1978) proved Ray and Singer's conjecture that Reidemeister torsion and analytic torsion are...
and only if P is a torsion point, the Bogomolov conjecture generalises the Manin-Mumford conjecture. The original Bogomolov conjecture was proved by Emmanuel...
are of finite order (a torsion point) in J, unless C = J. There are other more general versions, such as the Bogomolov conjecture which generalizes the...
realizable and that others were not. He essentially formulated the torsionconjecture for elliptic curves over the rational numbers, providing a complete...
SYZ conjecture is an attempt to understand the mirror symmetry conjecture, an issue in theoretical physics and mathematics. The original conjecture was...
Hanna Neumann conjecture implies another long-standing group-theoretic conjecture which says that every one-relator group with torsion is coherent (that...
generally torsion-free hyperbolic groups, are stable. Free groups on more than one generator are not superstable. The Cherlin–Zilber conjecture (also called...
September 2019) was an American mathematician who introduced the Zucker conjecture, proved in different ways by Eduard Looijenga (1988) and by Leslie Saper...
Mordell–Weil groups over Q have the same torsion groups belong to a parametrized family. The Birch and Swinnerton-Dyer conjecture (BSD) is one of the Millennium...
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