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The Motivic Cofiber Of Τ And Exotic Periodicities, Bogdan Gheorghe

Wayne State University Dissertations

Consider the Tate twist τ ∈ H 0,1 (S 0,0 ) in the mod 2 cohomology of the motivic sphere.

After 2-completion, the motivic Adams spectral sequence realizes this element as a map

τ : S 0,−1 GGA S 0,0 . This thesis begins with the study of its cofiber, that we denote by Cτ.

We first show that this motivic 2-cell complex can be endowed with a unique E ∞ ring

structure. This promotes the known isomorphism π ∗,∗ Cτ ∼= Ext ∗,∗ BP ∗ BP (BP ∗ ,BP ∗ )

to an isomorphism of rings which also preserves …