Quasi-elliptic cohomology and its power operations

Power Operations in Elliptic Cohomology and Representations of Loop Groups

The first part describes power operations in elliptic cohomology in terms of isogenies of the underlying elliptic curve. The second part discusses a relationship between equivariant elliptic cohomology and representations of loop groups. The third part investigates the representation theoretic considerations which give rise to the power operations discussed in the first part.

Reduced Power Operations in Motivic Cohomology

1 Reduced power operations in motivic cohomology

Quasi-quadratic elliptic curve point counting using rigid cohomology

We present a deterministic algorithm that computes the zeta function of a nonsupersingular elliptic curve E over a finite field with p elements in time quasi-quadratic in n. An older algorithm having the same time complexity uses the canonical lift of E, whereas our algorithm uses rigid cohomology combined with a deformation approach. An implementation in small odd characteristic turns out to g...

Isogenies of Supersingular Elliptic Curves over Finite Fields and Operations in Elliptic Cohomology

In this paper we investigate stable operations in supersingular elliptic cohomology using isogenies of supersingular elliptic curves over nite elds. Our main results provide a framework in which we give a conceptually simple new proof of an elliptic cohomology version of the Morava change of rings theorem and also gives models for explicit stable operations in terms of isogenies and morphisms i...