In mathematics, the Manin conjecture 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...

information (as is typical of several complex variables). The Manin–Mumford conjecture of Yuri Manin and David Mumford, proved by Michel Raynaud, states that...

Goldbach's conjecture The twin prime conjecture The Collatz conjecture The Manin conjecture The Maldacena conjecture The Euler conjecture, proposed by...

André–Oort conjecture is a problem in Diophantine geometry, a branch of number theory, that can be seen as a non-abelian analogue of the Manin–Mumford conjecture...

conjecture Kelvin's conjecture Kouchnirenko's conjecture Mertens conjecture Pólya conjecture, 1919 (1958) Ragsdale conjecture Schoenflies conjecture (disproved...

has a regular (i.e. with polynomial components) inverse function. Manin conjecture on the distribution of rational points of bounded height in certain...

principle to solve some problems is limited by the Manin obstruction, but for the Erdős–Straus conjecture this obstruction does not exist. On the face of...

implies that the set of k-rational points is Zariski dense in X.) The Manin conjecture is a more precise statement that would describe the asymptotics of...

more general conjectures have been put forth by Paul Vojta. The Mordell conjecture for function fields was proved by Yuri Ivanovich Manin and by Hans Grauert...

mapping class group, proved by Ib Madsen and Michael Weiss. The Manin-Mumford conjecture about Jacobians of curves, proved by Michel Raynaud. This disambiguation...

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b,...

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...

Zilber–Pink conjecture is a far-reaching generalisation of many famous Diophantine conjectures and statements, such as André–Oort, Manin–Mumford, and...

p-curvature conjecture, Nicholas Katz proved that the class of Gauss–Manin connections with algebraic number coefficients satisfies the conjecture. This result...

In mathematics, the Grothendieck–Katz p-curvature conjecture is a local-global principle for linear ordinary differential equations, related to differential...

zeta-function, including the Riemann hypothesis. Manin–Mumford conjecture The Manin–Mumford conjecture, now proved by Michel Raynaud, states that a curve...

of rational points on algebraic varieties, such as the Manin conjecture and Vojta's conjecture, have far-reaching implications for problems in Diophantine...

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 is a conjecture, named after Fedor Bogomolov, in arithmetic geometry about algebraic curves that generalizes the Manin–Mumford conjecture in...

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...

Nevanlinna invariant and it is conjectured that they are essentially the same. More precisely, Batyrev–Manin conjectured the following. Let X be a projective...

conjecture for K-groups of number rings, the Hodge conjecture, the Tate conjecture about algebraic cycles, the Birch and Swinnerton-Dyer conjecture about...

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...

zero-divisor conjecture implies the idempotent conjecture and is implied by the unit conjecture. As of 2021, the zero divisor and idempotent conjectures are open...

the Malcev algebra Yuri Manin, author of the Gauss–Manin connection in algebraic geometry, Manin-Mumford conjecture and Manin obstruction in diophantine...

Rueil-Malmaison, France. In 1983, Raynaud published a proof of the Manin–Mumford conjecture. In 1985, he proved Raynaud's isogeny theorem on Faltings heights...

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...

respectively, the Manin–Mumford conjecture, proven by Michel Raynaud, and the Mordell–Lang conjecture, proven by Gerd Faltings. The following conjectures illustrate...

field K of W rather than W. The Dieudonné–Manin classification theorem was proved by Dieudonné (1955) and Manin (1963). It describes the structure of F-isocrystals...