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www.galoisrepresentations.com | ||
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totallydisconnected.wordpress.com
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| | | | | $latex \bullet$ Let $latex f$ be some cuspidal Hecke eigenform, with associated Galois representation $latex \rho_{f}:G_{\mathbf{Q}}\to \mathrm{GL}_2(\overline{\mathbf{Q}_p})$. A notorious conjecture of Greenberg asserts that if $latex \rho_{f}|G_{\mathbf{Q}_p}$ is abelian (i.e. is a direct sum of characters), then $latex f$ is a CM form, or equivalently $latex \rho_f$ is induced from a character. At some point... | |
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quomodocumque.wordpress.com
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| | | | | As the old joke goes, "Who's that guy next to Mazur?" Barry Mazur, my Ph.D. advisor, was awarded the National Medal of Science last week. It's hard to overstate the extent to which his work and his outlook have affected the direction of number theory. And of course my own way of doing math is... | |
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www.jeremykun.com
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| | | | | Last time we defined and gave some examples of rings. Recapping, a ring is a special kind of group with an additional multiplication operation that "plays nicely" with addition. The important thing to remember is that a ring is intended to remind us arithmetic with integers (though not too much: multiplication in a ring need not be commutative). We proved some basic properties, like zero being unique and negation being well-behaved. | |
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alok.github.io
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| | | Alok Singh's Blog | ||
