CORDIS Project
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This project aims to advance the understanding of the Birch-Swinnerton-Dyer conjecture, a significant unsolved problem in mathematics. By constructing new examples of Euler systems, the research seeks to establish new cases of the conjecture related to elliptic curves.
The Birch--Swinnerton-Dyer conjecture, one of the Millennium Prize Problems, is one of the central unsolved problems in mathematics.
It predicts a relation between the arithmetic of an elliptic curve and the properties of the L-function of the elliptic curve.
Some special cases of the conjecture were proven by Kolyvagin; the main ingredient in his proof is an algebraic construction called an Euler system.
Even though Euler systems are extremely powerful tools, so far only five examples are known…
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