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Remark on the rank of elliptic curves

Igor Nikolaev

Institutional Repositories DataBase (IRDB) · 2009 · 11 citations · 11 references

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Abstract

A covariant functor on the elliptic curves with complex multiplication is constructed.The functor takes values in the noncommutative tori with real multiplication.A conjecture on the rank of an elliptic curve is formulated.

References

11

On the geometry and dynamics of diffeomorphisms of surfaces

William P. Thurston · Bulletin of the American Mathematical Society · 1988 · 1.1K citations · Full text

, , +9

<i>C</i><sup>∗</sup>-algebras associated with irrational rotations

Marc A. Rieffel · Pacific Journal of Mathematics · 1981 · 617 citations · Full text

, , +8

Quadratic differentials and foliations

John H. Hubbard, Howard Masur · Acta Mathematica · 1979 · 376 citations · Full text

, , +12

Categories of Holomorphic Vector Bundles on Noncommutative Two-Tori

Alexander Polishchuk, Albert Schwarz · Communications in Mathematical Physics · 2003 · 106 citations · Full text

, , +9

Real Multiplication and noncommutative geometry

Yuri I. Manin · ArXiv.org · 2002 · 83 citations · Full text

, , +14