| EPSRC Reference: |
EP/J018716/1 |
| Title: |
p-adic Iwasawa theory for Galois representations |
| Principal Investigator: |
Zerbes, Professor S |
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| Department: |
Mathematics |
| Organisation: |
UCL |
| Scheme: |
First Grant - Revised 2009 |
| Starts: |
01 September 2012 |
Ends: |
31 August 2014 |
Value (£): |
90,156
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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| Panel History: |
| Panel Date | Panel Name | Outcome |
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04 Jul 2012
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Mathematics Prioritisation Panel Meeting July 2012
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Announced
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Summary on Grant Application Form |
Iwasawa theory is a subfield of number theory whose fundamental questions relate arithmetic problems (e.g. rational solutions to polynomial equations in several variables) to analytic information (e.g. values of certain complex-analytic functions, so-called L-functions). The merging of these two disparate ideas makes Iwasawa theory a mysterious and powerful field. Via its main conjectures, Iwasawa theory remains the only systematic method known today for studying the deep connections between the arithmetic problems and special values of L-functions, typified by the conjecture of Birch and Swinnerton-Dyer.
One can use Iwasawa theory to study the arithmetic of elliptic curves, which are a class of polynomial equations in two variables. Questions about the arithmetic of elliptic curves are linked to some of the oldest problems in number theory, such as the congruent number problem which concerns the existence of right-angled triangles with certain properties. Elliptic curves also played a central role in Wiles' proof of Fermat's last theorem.
In the proposed research I plan to investigate some aspects of the Iwasawa theory of elliptic curves using recently developed tools from an another area of mathematics called 'p-adic analysis'. This should give new insight into some important problems (such as the Birch--Swinnerton-Dyer conjecture) in algebraic number theory.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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