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    • Sign (di)Lemma for Dimension Shifting

      Nitin Nitsure

      Volume 119 Issue 2 April 2009 pp 179-186

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/119/02/0179-0186

    • Keywords

       

      Abelian categories; derived functors; dimension shifting.

    • Abstract

       

      There is a surprising occurrence of some minus signs in the isomorphisms produced in the well-known technique of dimension shifting in calculating derived functors in homological algebra. We explicitly determine these signs. Getting these signs right is important in order to avoid basic contradictions. We illustrate the result – which we call as the sign lemma for dimension shifting – by some de Rham cohomology and Chern class considerations for compact Riemann surfaces.

    • Author Affiliations

       

      Nitin Nitsure1

      1. School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India

    • Dates

       
      Published
      April 2009
      Manuscript received
      15 June 2007
      Manuscript revised
      27 January 2008

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