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Verschiebung and Frobenius operators

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An Erratum to this article was published on 01 December 1990

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Abstract

Metropolis and Rota introduced the concept of the necklace ring Nr(A) of a commutative ringA. WhenA contains Q as a subring there is a natural bijection γ:Nr(A→1+tA[]. Grothendieck has introduced a ring structure on 1+tA[t] while studyingK-theoretic Chern classes. Nr(A) comes equipped with two families of operatorsF r,V r called the Frobenius and Verschiebung operators. Mathematicians studying formal group laws have introduced two families of operators,F r, andV r on 1+tA[t]. Metropolis and Rota have not however tried to show that γ preserves, these operators. They transport the operators from Nr(A) to 1+tA[t] using γ. In our present paper we show that γ does preserve all these operators.

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  • 01 December 1990

    Lines 4 and 5 on page 39

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Authors and Affiliations

  1. University of Calgary, T2N 1N4, Calgary, Alberta, Canada

    K Varadarajan

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  1. K Varadarajan
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Part of this work was done while the author was visiting the Institute of Mathematical Sciences, Madras.

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Varadarajan, K. Verschiebung and Frobenius operators. Proc. Indian Acad. Sci. (Math. Sci.) 100, 37–43 (1990). https://doi.org/10.1007/BF02881112

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