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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
10
votes
0
answers
228
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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 …
- 7,377
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
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