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quomodocumque.wordpress.com | ||
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www.galoisrepresentations.com
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| | | | | [AI summary] The blog post discusses a mathematical problem related to the surjectivity of certain maps in the context of Galois representations and modular forms. It references a conjecture about the structure of the mod-p deformation ring and its connection to the Hecke algebra. The author explores the implications of this conjecture on the properties of the deformation ring and its relation to the cohomology of arithmetic groups. The post also touches on the use of completed cohomology and the patched module in understanding these structures. The author acknowledges the complexity of the problem and the need for further research and collaboration to resolve it. | |
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mattbaker.blog
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| | | | | In my previous post, I presented a proof of the existence portion of the structure theorem for finitely generated modules over a PID based on the Smith Normal Form of a matrix. In this post, I'd like to explain how the uniqueness portion of that theorem is actually a special case of a more general... | |
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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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boldandgreen.wordpress.com
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| | | I tried a new background color for my windows as shown here. Instead of the light grey suggested, I picked a very light brown: R 230 Y 222 B 188 (as shown on picture). The best thing is to change the background in Word first and test the color. | ||
