Explore the words cloud of the Euler systems project. It provides you a very rough idea of what is the project "Euler systems" about.
The following table provides information about the project.
UNIVERSITY COLLEGE LONDON
|Coordinator Country||United Kingdom [UK]|
|Total cost||1˙070˙473 €|
|EC max contribution||1˙070˙473 € (100%)|
1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
|Duration (year-month-day)||from 2015-07-01 to 2020-06-30|
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|1||UNIVERSITY COLLEGE LONDON||UK (LONDON)||coordinator||1˙070˙473.00|
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 to exist. I propose to construct several new examples of Euler systems, in order to prove new cases of the Birch--Swinnerton-Dyer conjecture. In particular, I believe the following theorem to be within reach:
Let A be either a modular elliptic curve over a (real or imaginary) quadratic number field, or a modular abelian surface over the rational numbers. If the L-value L(A, 1) is non-zero, then the Mordell--Weil group of A is finite (i.e. the Birch--Swinnerton-Dyer conjecture holds for A).
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The information about "EULER SYSTEMS" are provided by the European Opendata Portal: CORDIS opendata.
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