The congruent number problem and the Birch-Swinnerton-Dyer conjecture

Agostino Prástaro

The congruent number problem and the Birch-Swinnerton-Dyer conjecture

General Mathematics 2015-05-05 v2

Authors: Agostino Prástaro

Abstract

By introducing a new point of view in Algebraic Topology relating elliptic curves in $\mathbb{R}^2$ and suitable bordism groups, the congruent number problem is solved showing that the Tunnell's theorem is also sufficient. This could be considered also an indirect proof that the Birch Swinnerton-Dyer conjecture is true.

Keywords

congruent number problem Birch-Swinnerton-Dyer conjecture elliptic curves bordism groups algebraic topology Tunnell's theorem sufficient condition

Cite

@article{arxiv.1504.07507,
  title  = {The congruent number problem and the Birch-Swinnerton-Dyer conjecture},
  author = {Agostino Prástaro},
  journal= {arXiv preprint arXiv:1504.07507},
  year   = {2015}
}

Comments

35 pages, 4 figures

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