Studies in Duality on Noetherian Formal Schemes and Non-Noetherian Ordinary Schemes

Released on by Leovigildo Alonso Tarrío
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  • Studies in Duality on Noetherian Formal Schemes and Non-Noetherian Ordinary Schemes Book Detail

  • Author : Leovigildo Alonso Tarrío
  • Release Date : 1999
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 138
  • ISBN 13 : 0821819429
  • File Size : 93,93 MB
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Studies in Duality on Noetherian Formal Schemes and Non-Noetherian Ordinary Schemes by Leovigildo Alonso Tarrío PDF Summary

Book Description: This volume contains three papers on the foundations of Grothendieck duality on Noetherian formal schemes and on not-necessarily-Noetherian ordinary schemes. The first paper presents a self-contained treatment for formal schemes which synthesizes several duality-related topics, such as local duality, formal duality, residue theorems, dualizing complexes, etc. Included is an exposition of properties of torsion sheaves and of limits of coherent sheaves. A second paper extends Greenlees-May duality to complexes on formal schemes. This theorem has important applications to Grothendieck duality. The third paper outlines methods for eliminating the Noetherian hypotheses. A basic role is played by Kiehl's theorem affirming conservation of pseudo-coherence of complexes under proper pseudo-coherent maps. This work gives a detailed introduction to the subject of Grothendieck Duality. The approach is unique in its presentation of a complex series of special cases that build up to the main results.

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