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Results tagged with algebraic-number-theory
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user 65
Algebraic number fields, Algebraic integers, Arithmetic Geometry, Elliptic Curves, Function fields, Local fields, Arithmetic groups, Automorphic forms, zeta functions, $L$-functions, Quadratic forms, Quaternion algebras, Homogenous forms, Class groups, Units, Galois theory, Group cohomology, Étale cohomology, Motives, Class field theory, Iwasawa theory, Modular curves, Shimura varieties, Jacobian varieties, Moduli spaces
5
votes
If Spec Z is like a Riemann surface, what's the analogue of integration along a contour?
For a number $f$ the local-global formula written as
$$
f_2\cdot f_3\cdot \dotsb \cdot f_{\mathbb Q} = 1
$$
where $f_p$ is the inverse power of $p$ that is equal to $f$ in the local field of $p$-adi …
- 15.1k
7
votes
1
answer
554
views
Hasse principle for a group
$\DeclareMathOperator\PSL{PSL}$In the paper Ono - "Hasse principle" for $\PSL_2 (\mathbb Z)$ and $\PSL_2(\mathbb F)$ there's a definition of a Hasse principle for a group $G$, but I don't completely g …
- 15.1k
5
votes
"Understanding" $\mathrm{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})$
I'm far from expect in this topic, but here's my attempt.
First, and that's something quite straightforward, people want to study Gal Q (this is how I will denote it; this common shortcut is defined …
- 15.1k