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Euler systems SIGNED

Euler systems and the Birch--Swinnerton-Dyer conjecture

Total Cost €

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EC-Contrib. €

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Partnership

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Project "Euler systems" data sheet

The following table provides information about the project.

Coordinator
UNIVERSITY COLLEGE LONDON 

Organization address
address: GOWER STREET
city: LONDON
postcode: WC1E 6BT
website: n.a.

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country United Kingdom [UK]
 Total cost 1˙070˙473 €
 EC max contribution 1˙070˙473 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2014-CoG
 Funding Scheme ERC-COG
 Starting year 2015
 Duration (year-month-day) from 2015-07-01   to  2020-06-30

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    UNIVERSITY COLLEGE LONDON UK (LONDON) coordinator 1˙070˙473.00

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 Project objective

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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