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Periodicity In Iterated Algebraic K-Theory Of Finite Fields, Gabriel Angelini-Knoll

Wayne State University Dissertations

In this dissertation, we study the interactions between periodic phenomena in the homotopy groups of spheres and algebraic K-theory of ring spectra. C. Ausoni and J. Rognes initiated a program to study the arithmetic of ring spectra using algebraic K-theory and gave a higher chromatic version of the Lichtenbaum-Quillen conjecture, called the red-shift conjecture, that is expected to govern this arithmetic. This dissertation provides a proof of a special case of a variation on the red-shift conjecture. Specifically, we show that, under conditions on the order of the fields, iterated algebraic K-theory of finite fields detects a periodic family chromatic …