Skip to main content
MathOverflow

Return to Question

latex
Source Link
M.G.
M.G.
  • 7.1k
  • 3
  • 46
  • 60

For an abelian surface $A/\mathbb{Q}$ such that $R:=$End$_{\mathbb{Q}}(A)$$R:=\mathrm{End}_{\mathbb{Q}}(A)$ is an order in a real quadratic field $K$ (so a GL$_2$$\mathrm{GL}_2$-type surface), is there a bound on the index $[O_K : R]$ of the ring inside the maximal order $O_K$?

For an abelian surface $A/\mathbb{Q}$ such that $R:=$End$_{\mathbb{Q}}(A)$ is an order in a real quadratic field $K$ (so a GL$_2$-type surface), is there a bound on the index $[O_K : R]$ of the ring inside the maximal order $O_K$?

For an abelian surface $A/\mathbb{Q}$ such that $R:=\mathrm{End}_{\mathbb{Q}}(A)$ is an order in a real quadratic field $K$ (so a $\mathrm{GL}_2$-type surface), is there a bound on the index $[O_K : R]$ of the ring inside the maximal order $O_K$?

Source Link
Sun Ra
Sun Ra
  • 173
  • 2

Index of the endomorphism ring of an abelian surface

For an abelian surface $A/\mathbb{Q}$ such that $R:=$End$_{\mathbb{Q}}(A)$ is an order in a real quadratic field $K$ (so a GL$_2$-type surface), is there a bound on the index $[O_K : R]$ of the ring inside the maximal order $O_K$?