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Results tagged with abelian-varieties
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user 110362
Abelian varieties are projective algebraic varieties endowed with an Abelian group structure. Over the complex numbers, they can be described as quotients of a vector space by a lattice of full rank. They are analogs in higher dimensions of elliptic curves, and play an important role in algebraic geometry and number theory.
3
votes
Accepted
About the type of a polarization of an abelian variety
Let $\lambda: A\rightarrow A^{\vee}$ be any polarization of degree prime to the characteristic, not necessarily self-dual.
There exists an $\lambda^{\vee} : A^{\vee}\rightarrow A$ such that $\lambda^{ …
- 984
8
votes
If it quacks like an abelian variety over a finite field
One possible answer to this could be Lang's theorem: it says that if $G/\mathbb{F}_q$ is a smooth connected algebraic group, then $H^1(\mathbb{F}_q,G)$ is trivial, or otherwise put every $G$-torsor ha …
- 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