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16
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3answers
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An unfamiliar (to me) form of Hensel's Lemma

In his very nice article Peter Roquette, History of valuation theory. I. (English summary) Valuation theory and its applications, Vol. I (Saskatoon, SK, 1999), 291--355, Fields Inst. Commun., ...
14
votes
4answers
2k views

Special values of $p$-adic $L$-functions.

This is a very naive question really, and perhaps the answer is well-known. In other words, WARNING: a non-expert writes. My understanding is that nowadays there are conjectures which essentially ...
19
votes
8answers
3k views

$p$-adic integrals and Cauchy's theorem

A short version of my question is: Is there a $p$-adic theory of integration? Now let me expand a little further. In introductory texts such as Koblitz' book $p$-adic numbers,.. a bunch of $p$-adic ...
15
votes
3answers
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2-adic Coefficients of Modular Hecke Eigenforms.

Suppose that N is prime, and consider the normalized cuspidal Hecke eigenforms of weight 2 and level Gamma_0(N). For such an eigenform f, the coefficients generate ...
7
votes
2answers
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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 ...