Questions tagged [iwasawa-theory]
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8 questions from the last 365 days
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Selmer complex and total complex
Thanks for your reading. I'm studying Selmer complex book by Jan Nekovar. For the definition of Selmer complex I meet a problem.
In the introduction(page 9, 0.8.0) the author gives us a definition of ...
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Arithmetic application: Complete group ring and group ring for infinite group
Let $G$ be a profinite(infinite) group, $\Lambda$ be the complete group ring(Iwasawa algerbra) of $G$ over a unity ring $R$. My first question is that do we know something about the relation with $\...
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Growth of invariants in mod-$p$ representations of $\mathrm{GL}_n$
Let $G$ be smooth admissible mod-$p$ representations of $\mathrm{GL}_n(\mathbb{Q}_p)$. Also suppose $\pi$ is an irreducible infinite-dimensional smooth admissible representation of $G$ over $\mathbb{F}...
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Could I get an interpretation for application of Euler characteristics in number theory？
As a beginner who just get in touch with Euler characteristics in this field, could I get some intuition for the arithmetic meaning of Euler characteristics of bounded complexes, for example Selmer ...
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On a sentence of J.Nekovar in the introduction of "Selmer complexes"
In his famous book "Selmer complexes", J.Nekovar, speaking about Greenberg conditions, wrote the following sentence (see 0.8.1 p.10)
these are the only local conditions that can be handled ...
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Indices of norms of units in a tower of a $\mathbb{Z}_p$-extension, or equivalently, order of $H^1$ of units in the tower
Let $K$ be a finite extension of $\mathbb{Q}$ and $L/K$ be a $\mathbb{Z}_p$-extension with finite layers $L_i$, hence $L_j/L_i$ is cyclic of order $p^{j-i}$ (put $K=L_0$). Let $U_E$ be the unit group ...
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Is there something I am missing about the computation of the $p$-part of the class groups of cyclotomic fields?
Well, the answer of the question in the title in certainly Yes, many things in fact, but let me be more precise.
In 1958, Serre gave a Bourbaki talk on the recent works of Iwasawa on class groups in ...
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How is Taylor-Wiles patching "horizontal Iwasawa theory"?
I have recently been reading into the proof of modularity of semistable elliptic curves, in particular (what is now known as) the Taylor-Wiles patching argument used to prove the $R=T$ theorem in the ...
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