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Results tagged with algebraic-number-theory
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user 110362
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
3
votes
Accepted
Integers in residue classes $\mathcal{O}_K/\mathfrak{p}$
Let $p$ be the prime number that satisfies $p\mathbb{Z} = \mathbb{Z} \cap \mathfrak{p}$.
Then your claim is equivalent to the inclusion $\mathbb{F}_p\subset \mathcal{O}_K/\mathfrak{p}$ being an equali …
- 984
5
votes
1
answer
311
views
Conductor at 2 of abelian surfaces with real multiplication
Let $A/\mathbb{Q}$ be an abelian surface such that $\text{End}_{\mathbb{Q}}(A)\otimes \mathbb{Q}$ is a real quadratic field $E$. I am interested in bounding the conductor of $A$ at $2$.
Let $\mathfrak …
- 984
10
votes
0
answers
228
views
If $H$ is a quotient of $G$, does there exist an $H$-extension of $\mathbb{Q}$ not contained...
Let $\phi\colon G\rightarrow H$ be a surjective homomorphism between finite groups. Assume that $\phi$ is not split, in other words there exists no homomorphism $\sigma\colon H\rightarrow G$ such that …
- 984