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词条 Parshin chain
释义

  1. References

In number theory, a Parshin chain is a higher-dimensional analogue of a place of an algebraic number field. They were introduced by {{harvtxt|Parshin|1978}} in order to define an analogue of the idele class group for 2-dimensional schemes.

A Parshin chain of dimension s on a scheme is a finite sequence of points p0, p1, ..., ps such that pi has dimension i and each point is contained in the closure of the next one.

References

  • {{Citation | last1=Kerz | first1=Moritz | title=Ideles in higher dimension | arxiv=0907.5337|mr=2831836 | year=2011 | journal=Mathematical Research Letters | issn=1073-2780 | volume=18 | issue=4 | pages=699–713 | doi=10.4310/mrl.2011.v18.n4.a9}}
  • {{Citation | last1=Parshin | first1=A. N. | authorlink=Aleksei Nikolaevich Parshin | title=Abelian coverings of arithmetic schemes |mr=514485 | year=1978 | journal=Doklady Akademii Nauk SSSR | issn=0002-3264 | volume=243 | issue=4 | pages=855–858}}
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1 : Algebraic number theory

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