{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T13:53:25Z","timestamp":1775138005518,"version":"3.50.1"},"reference-count":15,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T00:00:00Z","timestamp":1772928000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T00:00:00Z","timestamp":1772928000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Appl Categor Struct"],"published-print":{"date-parts":[[2026,4]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    We study the spectrum of closed subcategories in a quasi-scheme, i.e. a Grothendieck category\n                    <jats:italic>X<\/jats:italic>\n                    . The closed subcategories are the direct analogs of closed subschemes in the commutative case, in the sense that when\n                    <jats:italic>X<\/jats:italic>\n                    is the category of quasi-coherent sheaves on a quasi-projective scheme\n                    <jats:italic>S<\/jats:italic>\n                    , then the closed subschemes of\n                    <jats:italic>S<\/jats:italic>\n                    correspond bijectively to the closed subcategories of\n                    <jats:italic>X<\/jats:italic>\n                    . Many interesting quasi-schemes, such as the noncommutative projective scheme\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:tex-math>$$\\operatorname {Qgr-}\\hspace{-2.0pt}B = \\operatorname {Gr-}\\hspace{-2.0pt}B\/\\operatorname {Tors-}\\hspace{-2.0pt}B$$<\/jats:tex-math>\n                        <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                          <mml:mrow>\n                            <mml:mo>Qgr-<\/mml:mo>\n                            <mml:mspace\/>\n                            <mml:mi>B<\/mml:mi>\n                            <mml:mo>=<\/mml:mo>\n                            <mml:mo>Gr-<\/mml:mo>\n                            <mml:mspace\/>\n                            <mml:mi>B<\/mml:mi>\n                            <mml:mo>\/<\/mml:mo>\n                            <mml:mo>Tors-<\/mml:mo>\n                            <mml:mspace\/>\n                            <mml:mi>B<\/mml:mi>\n                          <\/mml:mrow>\n                        <\/mml:math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    associated to a graded algebra\n                    <jats:italic>B<\/jats:italic>\n                    , arise as quotient categories of simpler abelian categories. In this paper, we will show how to describe the closed subcategories of any quotient category\n                    <jats:italic>X<\/jats:italic>\n                    \/\n                    <jats:italic>Y<\/jats:italic>\n                    in terms of closed subcategories of\n                    <jats:italic>X<\/jats:italic>\n                    with special properties, when\n                    <jats:italic>X<\/jats:italic>\n                    is a category with a set of compact projective generators.\n                  <\/jats:p>","DOI":"10.1007\/s10485-026-09851-5","type":"journal-article","created":{"date-parts":[[2026,3,8]],"date-time":"2026-03-08T09:32:09Z","timestamp":1772962329000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Closed Subcategories of Quotient Categories"],"prefix":"10.1007","volume":"34","author":[{"given":"Daniel","family":"Rogalski","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,3,8]]},"reference":[{"issue":"2","key":"9851_CR1","doi-asserted-by":"publisher","first-page":"228","DOI":"10.1006\/aima.1994.1087","volume":"109","author":"M Artin","year":"1994","unstructured":"Artin, M., Zhang, J.J.: Noncommutative projective schemes. 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