{"id":909,"date":"2022-03-29T11:27:15","date_gmt":"2022-03-29T11:27:15","guid":{"rendered":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/?page_id=909"},"modified":"2022-07-04T11:12:26","modified_gmt":"2022-07-04T11:12:26","slug":"a-note-on-weakly-proregular-sequence","status":"publish","type":"page","link":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/a-note-on-weakly-proregular-sequence\/","title":{"rendered":"A note on weakly proregular sequence"},"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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A note on weakly proregular sequence<\/strong><\/em><\/em><\/p>\n<\/div>\n<\/div>\n\n\n\n

Ryoya Ando <\/strong><\/i>
Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science 2641
Yamazaki, Noda-shi, Chiba-ken, 278-8510, Japan.<\/p>\n\n\n\n

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Pages 98-107 | Received 04 August<\/span> 2021, Accepted 11 October 2021, Published 01 June<\/span> 2022 <\/span><\/p>\n\n\n\n

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

In this paper, we give an elementary proof of the result given by Schenzel that there are functorial isomorphisms between local cohomology groups and \u010cech cohomology groups, by using weakly proregular sequences. The existence of these isomorphisms was well-known for Noetherian rings, but he generalised it to non-Noetherian rings and gave necessary and sufficient conditions for cohomology to coincide. In [6], he used notions of derived category theory in his proof, but we do not use them in this paper. We give a proof within Abelian category theory.<\/p>\n\n\n\n

Keywords<\/strong>:<\/span>  Weakly proregular sequence, local cohomology, \u010cech cohomology. <\/p>\n\n\n\n

MSC numbers<\/strong>:<\/span> Primary 13D03; Secondary 13D45.<\/p>\n\n\n\n

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Moroccan Journal of Algebra and Geometry with Applications Latest articles A note on weakly proregular sequence Ryoya Ando Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science 2641 Yamazaki, Noda-shi, Chiba-ken, 278-8510, Japan. Pages 98-107 | Received 04 August 2021, Accepted 11 October 2021, Published 01 June 2022 Abstract In this paper, 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-909","page","type-page","status-publish","hentry","entry"],"_links":{"self":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/909","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=909"}],"version-history":[{"count":9,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/909\/revisions"}],"predecessor-version":[{"id":1118,"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/pages\/909\/revisions\/1118"}],"wp:attachment":[{"href":"https:\/\/ced.fst-usmba.ac.ma\/p\/mjaga\/wp-json\/wp\/v2\/media?parent=909"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}