Search Results
Search type | Search syntax |
---|---|
Tags | [tag] |
Exact | "words here" |
Author |
user:1234 user:me (yours) |
Score |
score:3 (3+) score:0 (none) |
Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
Views | views:250 |
Code | code:"if (foo != bar)" |
Sections |
title:apples body:"apples oranges" |
URL | url:"*.example.com" |
Saves | in:saves |
Status |
closed:yes duplicate:no migrated:no wiki:no |
Types |
is:question is:answer |
Exclude |
-[tag] -apples |
For more details on advanced search visit our help page |
Results tagged with reference-request
Search options not deleted
user 2481
This tag is used if a reference is needed in a paper or textbook on a specific result.
24
votes
Introductory text on Galois representations
There is a very nice introduction to Galois representations in chapter 9 of Diamond and Shurman's book "A First Course in Modular Forms". This is really thorough, e.g. it carefully explains the defini …
17
votes
Accepted
What is the Perrin-Riou logarithm (or regulator)?
I am sure I've already written an expository account of this somewhere, but I looked over the lecture and seminar notes on my webpage and couldn't find it, so I'll write one here instead.
Suppose we s …
17
votes
2
answers
2k
views
Why does Tate's conjecture imply semisimplicity of crystalline Frobenius?
I'm trying to find a reference for the following fact:
If Tate's conjecture is true for all smooth projective varieties over $\mathbb{F}_p$, then the Frobenius endomorphism on the crystalline coho …
14
votes
Accepted
BSD conjecture for rank 1 elliptic curves
The following theorem is due to Chris Skinner, in this 2014 paper.
Let E/Q be an elliptic curve such that rank E(Q) = 1 and the
Tate-Shafarevich group Sha(E / Q) is finite, and some other techni …
12
votes
Chow Groups of varieties over number fields
The statement you want follows fairly straightforwardly from Bass' conjecture -- sufficiently straightforwardly that it may well not have a separate name of its own.
If $\Sigma$ is a sufficiently lar …
11
votes
1
answer
773
views
Atkin--Lehner operators in Hida theory
Let $p$ be a prime, and $F$ a $p$-adic Hida family of ordinary modular forms (of some tame level $N \ge 1$). I'd like to know whether, for $q$ a prime factor of $N$, the actions of the Atkin--Lehner i …
10
votes
Accepted
Blueprint of L-functions and need for introducing them ( Hasse-Weil L-functions )
There is an excellent reason why the exponential term and the division by $n$ are there, although they look a bit mysterious at first.
Firstly, a correction to your formula: it should be $|C(\mathbb …
10
votes
Accepted
Reference request for Hecke operators for principal congruence subgroup of modular group
The reason why Hecke theory for $\Gamma(N)$ doesn't get much treatment in the literature is because you can easily reduce it to the $\Gamma_1(N)$ case. More precisely, you can conjugate $\Gamma(N)$ by …
9
votes
Reference request for Kato's paper: A generalization of local class field theory by using K ...
I found this old question while searching for Kato's paper myself. Just in case anyone else is also still looking for these, here's what I found.
Kato's work was published in three installments in J. …
8
votes
Accepted
Geometric interpretation of Iwasawa algebras: $\mathbb{Z}_p[[T]]$ as a disk?
The correct viewpoint is not "$\Lambda$ is like a disc", but "$\Lambda$ is like the functions on a disc".
To see this, ask yourself: given an element $f \in \mathbb{Z}_p[[T]]$, what values can we plug …
7
votes
Accepted
Good references for K-theory of modular curves?
I wouldn't recommend Beilinson's 1985 paper as a general reference -- it's terrifyingly compressed, developing an entire new subject in a single short paper, and crashes through the necessary material …
7
votes
Accepted
Origin of definitions of ramified Hecke operators
These operators certainly appeared in the 1970 paper by Atkin and Lehner:
Atkin, A. O. L.; Lehner, J. Hecke operators on $\Gamma_0(m)$. Math. Ann. 185
(1970), 134–160.
I don't know for sure th …
6
votes
Accepted
Rational Characters of a reductive group have the same rank as split component
This is much easier than it looks. The point is that any reductive group $G$ is isogenous to the product of its radical, which is its centre $Z(G)$, and its commutator subgroup, which is a semisimple …
6
votes
Class number of imaginary quadratic fields
The condition shouldn't be "$n$ is prime" but "$n$ is either 1, 2, or a prime congruent to 3 mod 4". For instance $\mathbb{Q}(-5)$ has class number 2.
The more general statement that the 2-torsion sub …
5
votes
Numerical evaluation of the Petersson product of elliptic modular forms
It's easy to reduce to the case of computing the Petersson product of a normalised new eigenform with itself. Here you can use the fact that the product is equal to the value at s=k of the symmetric s …