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Results tagged with algebraic-number-theory
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user 103423
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
7
votes
2
answers
503
views
Supersingular curves over $\mathbb{F}_q$ and the splitting of $p$
I'm looking at chapter 4 of Waterhouse's "Abelian varieties over finite fields"; and Theorems 4.1 and 4.2 seem to use the following fact:
Suppose that $E/\mathbb{F}_q$ is an elliptic curve over a fin …
- 901
3
votes
3
answers
760
views
Ramification of quaternion algebras over $\mathbb Q$
I'm reading on the classification of quaternion algebras over $\mathbb{Q}$. In the most common definition, we have a quaternion algebra $Q = \left(\frac{a,b}{\mathbb{Q}} \right)$ splits at a finite pr …
- 901