The Tate conjecture for a power of a CM elliptic curve

Abstract: The endomorphisms of an abelian variety $A$ over a field $k$ induce a natural decomposition of the Chow motive of $A$. For $E$ an elliptic curve over $k$ with complex multiplication, we explicitly describe the decomposition of the motive of $E^g$. When $k$ is finitely generated, we use the decomposition to prove the full Tate conjecture for $E^g$. When $k$ is a global function field, we formulate a version of the Beilinson-Bloch conjecture for varieties over $k$ and prove it in some special cases, including for powers of an isotrivial elliptic curve with all its endomorphisms defined over $k$.

algebraic geometrynumber theory

Audience: researchers in the topic

Boston University Number Theory Seminar