Rational points of bounded height outside the 27 lines on Clebsch's diagonal cubic surface.
In mathematics, the Manin conjecture describes the conjectural distribution of rational points on an algebraic variety relative to a suitable height function. It was proposed by Yuri I. Manin and his collaborators[1] in 1989 when they initiated a program with the aim of describing the distribution of rational points on suitable algebraic varieties.
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Franke, J.; Manin, Y. I.; Tschinkel, Y. (1989). "Rational points of bounded height on Fano varieties". Inventiones Mathematicae. 95 (2): 421–435. doi:10.1007/bf01393904. MR 0974910. Zbl 0674.14012.
In mathematics, the Maninconjecture describes the conjectural distribution of rational points on an algebraic variety relative to a suitable height function...
Manin died on 7 January 2023. Manin's early work included papers on the arithmetic and formal groups of abelian varieties, the Mordell conjecture in...
Goldbach's conjecture The twin prime conjecture The Collatz conjecture The Maninconjecture The Maldacena conjecture The Euler conjecture, proposed by...
information (as is typical of several complex variables). The Manin–Mumford conjecture of Yuri Manin and David Mumford, proved by Michel Raynaud, states that...
conjecture is a conjecture, named after Fedor Bogomolov, in arithmetic geometry about algebraic curves that generalizes the Manin-Mumford conjecture in...
has a regular (i.e. with polynomial components) inverse function. Maninconjecture on the distribution of rational points of bounded height in certain...
In mathematics, the main conjecture of Iwasawa theory is a deep relationship between p-adic L-functions and ideal class groups of cyclotomic fields, proved...
implies that the set of k-rational points is Zariski dense in X.) The Maninconjecture is a more precise statement that would describe the asymptotics of...
is unclear whether Manin's techniques will yield the actual proof. In 1980, Benedict Gross formulated the Gross–Stark conjecture, a p-adic analogue of...
mapping class group, proved by Ib Madsen and Michael Weiss. The Manin-Mumford conjecture about Jacobians of curves, proved by Michel Raynaud. This disambiguation...
of rational points on algebraic varieties, such as the Maninconjecture and Vojta's conjecture, have far-reaching implications for problems in Diophantine...
telescope conjecture for all heights greater than 1 and for all primes. This was the last outstanding conjecture among Ravenel's conjectures. The disproof...
zeta-function, including the Riemann hypothesis. Manin–Mumford conjecture The Manin–Mumford conjecture, now proved by Michel Raynaud, states that a curve...
evidence for the section conjecture", Lecture Notes in mathematics 2054, Springer 2013 (Habilitation thesis) "The Brauer–Manin obstruction for sections...
and Manin), which was explored and studied systematically by B. Dubrovin and Y. Zhang, A. Givental, C. Teleman and others. The Virasoro conjecture is a...
conjecture for K-groups of number rings, the Hodge conjecture, the Tate conjecture about algebraic cycles, the Birch and Swinnerton-Dyer conjecture about...
special classes of varieties, but not in general. Manin used the Brauer group of X to define the Brauer–Manin obstruction, which can be applied in many cases...
of Manin, the obstructions to the Hasse principle holding for cubic forms can be tied into the theory of the Brauer group; this is the Brauer–Manin obstruction...
algebro-geometric problems. Thus they gave a new proof of the Manin–Mumford conjecture (which was first proved by Michel Raynaud and Ehud Hrushovski)...
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