{"id":2220,"date":"2024-06-28T13:49:14","date_gmt":"2024-06-28T13:49:14","guid":{"rendered":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/?page_id=2220"},"modified":"2024-06-30T00:09:34","modified_gmt":"2024-06-30T00:09:34","slug":"an-accessible-calculation-of-the-stalks-of-the-structure-sheaf-of-the-affine-scheme-of-anintegral-domain","status":"publish","type":"page","link":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/an-accessible-calculation-of-the-stalks-of-the-structure-sheaf-of-the-affine-scheme-of-anintegral-domain\/","title":{"rendered":"An accessible calculation of the stalks of the structure sheaf of the affine scheme of an integral domain"},"content":{"rendered":"\n
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Moroccan Journal of Algebra and Geometry with Applications<\/strong><\/p>\n\n\n\n

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An accessible calculation of the stalks of the structure sheaf of the affine
<\/strong> scheme of an integral domain<\/strong><\/p>\n<\/div>\n<\/div>\n\n\n\n

David E. Dobbs <\/strong><\/i>
Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1320, USA.<\/p>\n\n\n\n

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Pages 1-22 | Received 26 June 2023, Accepted 19 September 2023, Published 30 June 2024 <\/span><\/p>\n\n\n\n

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Abstract<\/span><\/strong><\/p>\n\n\n\n

Assuming minimal background in algebra and topology, we give a proof that for a domain A<\/span>, the stalk of the structure sheaf of the affine scheme Spec(A)<\/span> at a point P<\/span> is A_P<\/span>. While being more accessible than the standard proof, the proof that is given here leaves few or no ambiguities or questions concerning the foundations of mathematics. Such ambiguities arise inevitably in the standard proof which considers, more generally, A<\/span> to be an arbitrary commutative ring with 1. An appendix surveys some of the history involving such ambiguities in the mathematical and philosophical literature of the past 100 years.<\/p>\n\n\n\n

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Keywords<\/strong>:<\/span>  Integral domain, Zariski topology, localization, stalk, sheaf, Hilbert symbol, direct limit, commutative ring.<\/p>\n\n\n\n

MSC numbers<\/strong>:<\/span> Primary 13G05, 13A15, 13B30, 14A05; Secondary 18A30, 03A05, 14A15.<\/p>\n\n\n\n

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Moroccan Journal of Algebra and Geometry with Applications Latest articles An accessible calculation of the stalks of the structure sheaf of the affine scheme of an integral domain David E. Dobbs  Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996-1320, USA. Pages 1-22 | Received 26 June 2023, Accepted 19 September 2023, Published 30 June Read More<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"template-page-builder.php","meta":{"footnotes":""},"class_list":["post-2220","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2220","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/comments?post=2220"}],"version-history":[{"count":9,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2220\/revisions"}],"predecessor-version":[{"id":2313,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/2220\/revisions\/2313"}],"wp:attachment":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/media?parent=2220"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}