2004Current Developments in MathematicsOpen access

Main Conjectures and Modular Forms

Christopher Skinner

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Abstract

This paper reports on joint work with E. Urban that completes a proof of the Main Conjecture of Iwasawa Theory for a broad class of elliptic curves and modular forms. As such, it is concerned mainly with special values of $L$-functions of modular forms and the ways which they get packaged together (such as in $p$-adic $L$-functions).

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What this paper is about

This paper reports on joint work with E. Urban that completes a proof of the Main Conjecture of Iwasawa Theory for a broad class of elliptic curves and modular forms. As such, it is concerned mainly with special values of $L$-functions of modular forms and the ways which they get packaged together (such as in $p$-adic $L$-functions).

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Available abstract

This paper reports on joint work with E. Urban that completes a proof of the Main Conjecture of Iwasawa Theory for a broad class of elliptic curves and modular forms. As such, it is concerned mainly with special values of $L$-functions of modular forms and the ways which they get packaged together (such as in $p$-adic $L$-functions).

Key concepts: Modular form, Modular design, Modular elliptic curve, Conjecture, Class (philosophy), Mathematics, Algebra over a field, Pure mathematics

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