Abstract
Building on results of Ando, Hopkins and Rezk, we show the existence of uncountably many -String orientations of real K-theory KO and of topological modular forms tmf, generalizing the - (resp. the Witten) genus. Furthermore, the obstruction to lifting an -String orientations from KO to tmf is identified with a classical Iwasawa-theoretic condition. The common key to all these results is a ...
Abstract
Building on results of Ando, Hopkins and Rezk, we show the existence of uncountably many -String orientations of real K-theory KO and of topological modular forms tmf, generalizing the - (resp. the Witten) genus. Furthermore, the obstruction to lifting an -String orientations from KO to tmf is identified with a classical Iwasawa-theoretic condition. The common key to all these results is a precise understanding of the classical Kummer congruences, imposed for all primes simultaneously. This result is of independent arithmetic interest.
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