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3
votes
2answers
193 views

Interpolation of periods for a Hida family of modular forms

Let $\mathbf{f}$ be a Hida family of ordinary $p$-adic modular forms, and let $V(\mathbf{f})$ be the corresponding $\Lambda$-adic Galois representation (a quotient of the inverse limit $$ ...
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votes
0answers
42 views

classical specializations of Hida families

Let 𝕋 denote the ordinary Λ-adic Hecke algebra of say tame level N. If $P_{F}$ minimal prime of 𝕋 correspond to hida families F and this family specialise to classical weight one ordinary modular ...
7
votes
2answers
475 views

Periods for 2-variable p-adic L-functions

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 ...
12
votes
2answers
535 views

Examples of q-expansions in a Hida family

Let $p$ be a prime number and $N$ a positive integer not divisible by $p$. For some easy choices of $p$ and $N$, can anybody provide me with explicit examples of collections $$\{f_k,\quad 2\leq k ...
7
votes
2answers
328 views

Non-classical specializations of Hida families

Let ${\mathbb T}$ denote the ordinary $\Lambda$-adic Hecke algebra of say tame level $N$. If I specialize ${\mathbb T}$ to a classical weight $k \geq 2$, then it is proven by Hida that the result is ...
7
votes
2answers
926 views

Free subquotient of Galois representations coming from Hida theory

Let $\mathbf{T}$ be the reduced nearly ordinary Hecke algebra of level $N$ of Hida theory for $\operatorname{GL}_{2}$ over $\mathbb{Q}$ (or more generally over a totally real field $F$). Then ...