In number theory, a Parshin chain is a higher-dimensional analogue of a place of an algebraic number field. They were introduced by 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
- Kerz, Moritz (2011), "Ideles in higher dimension", Mathematical Research Letters, 18 (4): 699–713, arXiv: 0907.5337, doi: 10.4310/mrl.2011.v18.n4.a9, ISSN 1073-2780, MR 2831836, S2CID 7625761
- Parshin, A. N. (1978), "Abelian coverings of arithmetic schemes", Doklady Akademii Nauk SSSR, 243 (4): 855–858, ISSN 0002-3264, MR 0514485
 | This number theory-related article is a stub. You can help Wikipedia by expanding it. |
In number theory, a Parshin chain is a higher-dimensional analogue of a place of an algebraic number field. They were introduced by 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
- Kerz, Moritz (2011), "Ideles in higher dimension", Mathematical Research Letters, 18 (4): 699–713, arXiv: 0907.5337, doi: 10.4310/mrl.2011.v18.n4.a9, ISSN 1073-2780, MR 2831836, S2CID 7625761
- Parshin, A. N. (1978), "Abelian coverings of arithmetic schemes", Doklady Akademii Nauk SSSR, 243 (4): 855–858, ISSN 0002-3264, MR 0514485
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| This number theory-related article is a stub. You can help Wikipedia by expanding it. |