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Results tagged with adeles
Search options questions only
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user 43737
12
votes
2
answers
308
views
Automorphic quotients for inner forms or $GSp(4)$
For a quaternion algebra $D$, introduce the quaternionic similitude unitary groups:
\begin{equation}
\mathrm{GU}_D = \left\{ g \in \mathrm{GL}(D) \ : \ g^\star
\left(
\begin{array}{cc}
& 1 \\
1 &
\en …
- 5,424
3
votes
2
answers
624
views
Compactness of the automorphic quotient
Let $F$ be a (totally real) number field, and $E$ a (totally imaginary) quadratic extension of $F$. We consider $U$ a unitary group (with respect to a given hermitian form over $E$). The question is:
…
- 5,424
0
votes
0
answers
105
views
Preimage of projection of idèles, and other usual maps
Let $K$ be a quadratic number field.
I am struggling with some "usual" maps in algebraic number theory, but with which I am not used to, confusing a lot of different settings, as idèles, correspondin …
- 5,424
1
vote
0
answers
287
views
Adelic integral factorization
say Schwartz-Bruhat) function, the following identity holds :
$$\int_{\mathbf{A}^2} f(x)dx = \int_{SL_2(\mathbf{A})/SL_2(K)} \left( \sum_{a \in K^2 - 0} f(ua) \right) du$$
where $\mathbf{A}$ are the adeles …
- 5,424
19
votes
1
answer
3k
views
A good book on adeles and ideles
Unfortunately I never found a good reference book for the adeles and ideles definitions and properties : they always are treated in appendix or in a little chapter giving most of the time only the necessary … Travelling among tens of lecture notes and books (Weil, Vignéras, Goldfeld, Lang, Milne, Tate, Bump, Gelbart, etc. : all books which have not adeles as main theme !) …
- 5,424