• Verschiebung and Frobenius operators

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      https://www.ias.ac.in/article/fulltext/pmsc/100/01/0037-0043

    • Keywords

       

      Necklace ring; unital power series ring; ring of Witt vectors

    • 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 operatorsFr,Vr called the Frobenius and Verschiebung operators. Mathematicians studying formal group laws have introduced two families of operators,Fr, andVr 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.

    • Author Affiliations

       

      K Varadarajan1

      1. University of Calgary, Calgary, Alberta - T2N 1N4, Canada
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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