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    • On ramification index of composition of complete discrete valuation fields

      PASUPULATI SUNIL KUMAR

      Article Volume 130 Published: 19 September 2020 Article ID 0056

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      https://www.ias.ac.in/article/fulltext/pmsc/130/0056

    • Keywords

       

      Complete discrete valuation fields; ramification indices; linearly disjoint extensions.

    • Abstract

       

      For an extension $L/K$ of discrete valuation fields, let $e_{L/K}$ , $\mathfrak{O}_L$ denote the ramification index and valuation ring of $L/K$ respectively. Let $K$ be a complete discrete valuation field and $L_1/K$, $L_2/K$ be finite linearly disjoint extensions over $K$. We show that if $\mathfrak{O}_{L_1L_2}=\mathfrak{O}_{L_1}\mathfrak{O}_{L2}$ or gcd$(e_{L_1/K} , e_{L_2/K}) = 1$, and one of the residue fields $l_1/k$, $l_2/k$ is separable, then $e_{L_1L_2/L_1}= e_{L_2/K}$. The analogous results for the residue degrees are also true.

    • Author Affiliations

       

      PASUPULATI SUNIL KUMAR1

      1. Indian Institute of Science Education and Research, Thiruvananthapuram 695 551, India

    • Dates

       
      Published
      19 September 2020
      Final version published online
      19 September 2020

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