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The spectrum of units of a height 2 theory

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HHHW03 - Derived algebraic geometry and chromatic homotopy theory

The space BSU admits two infinite loop space structures, one arising from addition of vector bundles and the other from tensor product. A surprising fact, due to Adams and Priddy, is that these two infinite loop spaces become equivalent after p-completion. I will explain how the Adams-Priddy theorem allows for an identification of sl_1(ku_p), the spectrum of units of p-complete complex K-theory. I will then describe work, joint with Andrew Senger, that attempts to similarly understand the spectrum of units of the 2-completion of tmf_1(3). Our computations seem suggestive of broader phenomena, and I will include discussion of several open questions.

This talk is part of the Isaac Newton Institute Seminar Series series.

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