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34925 results in Mathematics (general)

Page 86 of 1747

  • 7 - Heights over finitely generated fields

  • Edited by Pieter Belmans, Université du Luxembourg, Wei Ho, University of Michigan, Ann Arbor, Aise Johan de Jong, Columbia University, New York
  • Book:
    Stacks Project Expository Collection
    Published online:
    06 October 2022
    Print publication:
    27 October 2022, pp 222-254

  • Summary

    This is an expository account about height functions and Arakelov theory in arithmetic geometry. We recall Conrad’s description of generalized global fields in order to describe heights over function fields of higher transcendence degree. We then give a brief overview of Arakelov theory and arithmetic intersection theory. Our exposition culminates in a description of Moriwaki’s Arakelov-theoretic formulation of heights, as well as a comparison of Moriwaki’s construction to various versions of heights.

Recent Developments in Algebraic Geometry
  • To Miles Reid for his 70th Birthday
  • Edited by Hamid Abban, Gavin Brown, Alexander Kasprzyk, Shigefumi Mori
  • Published online:
    25 October 2022
    Print publication:
    03 November 2022
  • Written in celebration of Miles Reid's 70th birthday, this illuminating volume contains 11 papers by leading mathematicians in and around algebraic geometry, broadly related to the themes and interests of Reid's varied career. Just as in Reid's own scientific output, some of the papers give comprehensive accounts of the state of the art of foundational matters, while others give expositions of subject areas or techniques in concrete terms. Reid has been one of the major expositors of algebraic geometry and a great influence on many in this field – this book hopes to inspire a new generation of graduate students and researchers in his tradition.

Page 86 of 1747