(2026-06) The Generalised Tate Pairing over any field
2026-06-26
We generalise a pairing on elliptic curves over finite fields, called the generalised Tate pairing, which is defined in terms of an arbitrary endomorphism of the curve, with certain trace requirements. We rederive this pairing from group cohomology, which allows us to generalise the pairing to principally polarized abelian varieties over any field, endomorphisms of any trace, and prove perfectness using a general duality theorem.