Online Talk

After 45 years, we return to the Stable Adams Conjecture. We begin by briefly recalling proofs of the Adams Conjecture concerning the J-homomorphism from vector bundles to sphere fibrations. Efforts to prove an analogue of this conjecture in the stable homotopy category have involved challenges of independent interest. Our approach, then and now, utilizes Segal Γ-spaces as a model for stable homotopy theory.

We shall sketch a proof of revised formulations of this stable Adams Conjecture. Our proof employs the Frobenius map in characteristic p > 0 algebraic geometry,utilizing techniques which should have further applications.