Frobenius homomorphisms in higher algebra

  • Thomas Nikolaus

    FB Mathematik und Informatik, Universität Münster, Einsteinstr. 62, D-48149 Münster, Germany
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We will discuss versions of the Frobenius homomorphism for a ring spectrum : the Tate-valued Frobenius and the Frobenius on topological Hochschild homology . Similar to ordinary algebra, these morphisms play an important role in higher algebra and are related to various concepts in stable homotopy theory and algebraic -theory. We discuss the notion of perfectness, which is to say that these morphisms are equivalences, and relate this notion to the Segal conjecture, the red-shift conjecture, and the classification of spaces by stable data.