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I am just reading about Iwasawa theory about Coates and Sujatha's book on Iwasawa Theory. I was wondering that since Iwasawa thought about the whole theory from the analogy of curves over finite field …

Unfortunately the question I am asking isnt very well-defined. But I will try to make it as precise as possible. Supposed I am given a mod-p representation of $G_Q$ into $Gl_2(F_p)$. I want to check f …

I am reading about the L-functions of elliptic curves and I was thinking about the root number as the product of local root numbers. So my question is how to think about the local root numbers geometr …

My question is how should one think of p-adic L functions? I know they have been constructed classically by interpolating values of complex L-functions. Recently I have seen people think about them in …

The Bloch-Kato and Beilinson's conjectures. Here is an extremely pleasant write up on that http://www.claymath.org/programs/summer_school/2009/BellaicheNotes.pdf http://www.math.jussieu.fr/~nekovar/pu …

You can look up Iwasawa's old papers like Analogy between number and function fields which is pretty much the motivation for the subject. Also Iwasawa's book on p-adic L-functions is a hard but good b …

You can look up the nice paper by Manjul Bhargava and Kiran Kedlaya titled "Continuous functions on compact sets of local fields". The results in this paper are weaker than the papers proposed by othe …

I was reading about the conjecture made by Gouvea and Mazur in their paper "Families of modular eigenforms" which says that if $k_1 \equiv k_2 \pmod {p^{n}(p-1)}$ for some integer $n\geq \alpha$. then …

Hi, I am reading about p-adic representations from Fontaine's book which can be found at http://staff.ustc.edu.cn/~yiouyang/research.html. On page 145 where they prove Proposition 5.24 which is esse …

A theorem of Gouvea and Hida (or rather a consequence of it) states that there exist a Galois representation attached to a $p$-adic eigenform $f$ provided the residual representation attached to a cla …

Let f be a modular form of weight k for $\Gamma_0(N)$. Let us assume that $p\not\vert$N. Then we can construct 2 p-adic L-functions corresponding to the 2 roots $\alpha$ and $\beta$ of the equation $x …

Hi all, I am sorry to ask a stupid question but I am really confused right now. Kitagawa-Mazur constructed a $2$-variable p-adic L-function attached to Hida families of modular forms. For their con …