{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,11]],"date-time":"2023-10-11T04:36:55Z","timestamp":1696999015529},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2020,10,24]],"date-time":"2020-10-24T00:00:00Z","timestamp":1603497600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,10,24]],"date-time":"2020-10-24T00:00:00Z","timestamp":1603497600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Appl Categor Struct"],"published-print":{"date-parts":[[2021,4]]},"DOI":"10.1007\/s10485-020-09613-x","type":"journal-article","created":{"date-parts":[[2020,10,24]],"date-time":"2020-10-24T15:02:24Z","timestamp":1603551744000},"page":"213-233","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["The Homotopy Category of Cotorsion Flat Modules"],"prefix":"10.1007","volume":"29","author":[{"given":"Hossein","family":"Eshraghi","sequence":"first","affiliation":[]},{"given":"Ali","family":"Hajizamani","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,10,24]]},"reference":[{"issue":"2","key":"9613_CR1","doi-asserted-by":"publisher","first-page":"615","DOI":"10.1006\/jabr.2001.8821","volume":"243","author":"ST Aldrich","year":"2001","unstructured":"Aldrich, S.T., Enochs, E.E., Garcia Rozas, J.R., Oyonarte, L.: Covers and envelopes in Grothendieck categories: flat covers of complexes with applications. J. Algebra 243(2), 615\u2013630 (2001)","journal-title":"J. Algebra"},{"key":"9613_CR2","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1016\/j.jalgebra.2011.03.018","volume":"335","author":"J Asadollahi","year":"2011","unstructured":"Asadollahi, J., Bahlekeh, A., Hajizamani, A., Salarian, Sh: On certain homological invariants of groups. J. Algebra 335, 18\u201335 (2011)","journal-title":"J. Algebra"},{"issue":"2\u20133","key":"9613_CR3","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1016\/0022-4049(91)90144-Q","volume":"71","author":"LL Avramov","year":"1991","unstructured":"Avramov, L.L., Foxby, H.-B.: Homological dimensions of unbounded complexes. J. Pure Appl. Algebra 71(2\u20133), 129\u2013155 (1991)","journal-title":"J. Pure Appl. Algebra"},{"key":"9613_CR4","first-page":"1","volume":"100","author":"AA Beilinson","year":"1982","unstructured":"Beilinson, A.A., Bernstein, J., Deligne, P.: Faisceaux pervers. Asterisque 100, 1\u2013172 (1982)","journal-title":"Asterisque"},{"key":"9613_CR5","doi-asserted-by":"crossref","unstructured":"Beligiannis, A., Reiten, I.: Homological and homotopical aspects of torsion theories. Mem. Am. Math. Soc. 188(883), viii+207 pp (2007)","DOI":"10.1090\/memo\/0883"},{"issue":"4","key":"9613_CR6","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1017\/S0024609301008104","volume":"33","author":"L Bican","year":"2001","unstructured":"Bican, L., El Bashir, R., Enochs, E.: All modules have flat covers. Bull. Lond. Math. Soc. 33(4), 385\u2013390 (2001)","journal-title":"Bull. Lond. Math. Soc."},{"key":"9613_CR7","volume-title":"Homological Algebra","author":"H Cartan","year":"1956","unstructured":"Cartan, H., Eilenberg, S.: Homological Algebra. Princeton Univ. Press, Princeton (1956)"},{"issue":"1","key":"9613_CR8","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1006\/jabr.1998.7582","volume":"210","author":"EE Enochs","year":"1998","unstructured":"Enochs, E.E., Garc\u00eda Rozas, J.R.: Flat covers of complexes. J. Algebra 210(1), 86\u2013102 (1998)","journal-title":"J. Algebra"},{"key":"9613_CR9","doi-asserted-by":"publisher","DOI":"10.1515\/9783110803662","volume-title":"Relative Homological Algebra","author":"EE Enochs","year":"2000","unstructured":"Enochs, E.E., Jenda, O.M.G.: Relative Homological Algebra. Walter de Gruynter, Berlin (2000)"},{"issue":"8","key":"9613_CR10","doi-asserted-by":"publisher","first-page":"3369","DOI":"10.1090\/S0002-9947-04-03416-6","volume":"356","author":"J Gillespie","year":"2004","unstructured":"Gillespie, J.: The flat model structure on Ch(R). Trans. Am. Math. Soc. 356(8), 3369\u20133390 (2004)","journal-title":"Trans. Am. Math. Soc."},{"key":"9613_CR11","doi-asserted-by":"publisher","first-page":"859","DOI":"10.1016\/j.aim.2016.01.004","volume":"291","author":"J Gillespie","year":"2016","unstructured":"Gillespie, J.: Gorenstein complexes and recollements from cotorsion pairs. Adv. Math. 291, 859\u2013911 (2016)","journal-title":"Adv. Math."},{"issue":"1","key":"9613_CR12","doi-asserted-by":"publisher","first-page":"257","DOI":"10.4310\/HHA.2007.v9.n1.a11","volume":"9","author":"H Holm","year":"2007","unstructured":"Holm, H., J\u00f8rgensen, P.: Compactly generated homotopy categories. Homol. Homotopy Appl. 9(1), 257\u2013274 (2007)","journal-title":"Homol. Homotopy Appl."},{"issue":"3","key":"9613_CR13","doi-asserted-by":"publisher","first-page":"753","DOI":"10.1090\/S0002-9939-2012-11364-4","volume":"141","author":"E Hosseini","year":"2013","unstructured":"Hosseini, E., Salarian, Sh: A cotorsion theory in the homotopy category of flat quasi-coherent sheaves. Proc. Am. Math. Soc. 141(3), 753\u2013762 (2013)","journal-title":"Proc. Am. Math. Soc."},{"key":"9613_CR14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-82783-9","volume-title":"Cohomology of Sheaves. Universitext","author":"B Iversen","year":"1986","unstructured":"Iversen, B.: Cohomology of Sheaves. Universitext. Springer, Berlin (1986)"},{"issue":"1","key":"9613_CR15","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1016\/j.aim.2004.05.003","volume":"193","author":"P J\u00f8rgensen","year":"2005","unstructured":"J\u00f8rgensen, P.: The homotopy category of complexes of projective modules. Adv. Math. 193(1), 223\u2013232 (2005)","journal-title":"Adv. Math."},{"issue":"1","key":"9613_CR16","doi-asserted-by":"publisher","first-page":"59","DOI":"10.4171\/JEMS\/72","volume":"9","author":"P J\u00f8rgensen","year":"2007","unstructured":"J\u00f8rgensen, P.: Existence of Gorenstein projective resolutions and Tate cohomology. J. Eur. Soc. 9(1), 59\u201376 (2007)","journal-title":"J. Eur. Soc."},{"issue":"5","key":"9613_CR17","doi-asserted-by":"publisher","first-page":"1128","DOI":"10.1112\/S0010437X05001375","volume":"141","author":"H Krause","year":"2005","unstructured":"Krause, H.: The stable derived category of a Noetherian scheme. Compos. Math. 141(5), 1128\u20131162 (2005)","journal-title":"Compos. Math."},{"key":"9613_CR18","doi-asserted-by":"crossref","first-page":"669","DOI":"10.4171\/dm\/501","volume":"20","author":"H Krause","year":"2015","unstructured":"Krause, H.: Deriving Auslander\u2019s formula. Documenta Math. 20, 669\u2013688 (2015)","journal-title":"Documenta Math."},{"key":"9613_CR19","series-title":"Graduate Texts in Mathematics","volume-title":"Categories for the Working Mathematician","author":"S Mac Lane","year":"1998","unstructured":"Mac Lane, S.: Categories for the Working Mathematician. Graduate Texts in Mathematics, 2nd edn. Springer, New York (1998)","edition":"2"},{"key":"9613_CR20","unstructured":"Murfet, D.: The mock homotopy category of projectives and Grothendieck duality. Ph.D thesis, Australian National University (2007)"},{"issue":"5","key":"9613_CR21","doi-asserted-by":"publisher","first-page":"547","DOI":"10.24033\/asens.1659","volume":"25","author":"A Neeman","year":"1992","unstructured":"Neeman, A.: The connection between the K-theory localization theorem of Thomason, Trobaugh and Yao and the smashing subcategories of Bousfield and Ravenel. Ann. Sci. \u00c9cole Norm. Sup. (4) 25(5), 547\u2013566 (1992)","journal-title":"Ann. Sci. \u00c9cole Norm. Sup. (4)"},{"issue":"1","key":"9613_CR22","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1090\/S0894-0347-96-00174-9","volume":"9","author":"A Neeman","year":"1996","unstructured":"Neeman, A.: The Grothendieck duality theorem via Bousfield\u2019s techniques and Brown representability. J. Am. Math. Soc. 9(1), 205\u2013236 (1996)","journal-title":"J. Am. Math. Soc."},{"key":"9613_CR23","series-title":"Annals of Mathematics Studies","doi-asserted-by":"publisher","DOI":"10.1515\/9781400837212","volume-title":"Triangulated Categories","author":"A Neeman","year":"2001","unstructured":"Neeman, A.: Triangulated Categories. Annals of Mathematics Studies, vol. 148. Princeton University Press, Princeton (2001)"},{"key":"9613_CR24","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1007\/s00222-008-0131-0","volume":"174","author":"A Neeman","year":"2008","unstructured":"Neeman, A.: The homotopy category of flat modules, and Grothendieck duality. Invent. Math. 174, 255\u2013308 (2008)","journal-title":"Invent. Math."},{"issue":"2","key":"9613_CR25","doi-asserted-by":"publisher","first-page":"429","DOI":"10.2140\/ant.2014.8.429","volume":"8","author":"A Neeman","year":"2014","unstructured":"Neeman, A.: The homotopy category of injectives. Algebra Number Theory 8(2), 429\u2013456 (2014)","journal-title":"Algebra Number Theory"},{"key":"9613_CR26","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF01390094","volume":"13","author":"M Raynaud","year":"1971","unstructured":"Raynaud, M., Gruson, L.: Crit\u00e8res de platitude et de projectivit\u00e9. Techniques de \u201cplatification\u201d d$$^,$$un module. Invent. Math. 13, 1\u201389 (1971)","journal-title":"Invent. Math."},{"key":"9613_CR27","series-title":"Symposia Mathematica","first-page":"11","volume-title":"Cotorsion Theories for Abelian Groups","author":"L Salce","year":"1979","unstructured":"Salce, L.: Cotorsion Theories for Abelian Groups. Symposia Mathematica, vol. 23, pp. 11\u201332. Cambridge University Press, Cambridge (1979)"},{"key":"9613_CR28","first-page":"121","volume":"65","author":"N Spaltenstein","year":"1988","unstructured":"Spaltenstein, N.: Resolutions of unbounded complexes. Compos. Math. 65, 121\u2013154 (1988)","journal-title":"Compos. Math."},{"key":"9613_CR29","doi-asserted-by":"crossref","unstructured":"Verdier, J.L.: Cat\u00e9gories d\u00e8riv\u00e8es. quelques r\u00e8sultats \u00e9tat 0. In: SGA $$4\\frac{1}{2}$$, Lecture Notes in Math., vol. 569, pp. 262\u2013311. Springer, Berlin (1977)","DOI":"10.1007\/BFb0091525"},{"key":"9613_CR30","unstructured":"Verdier, J.L.: Des categories derivees des categories abeliennes. Asterisque 239 (1996)"},{"key":"9613_CR31","series-title":"Cambridge Studies in Advanced Mathematics","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139644136","volume-title":"An Introduction to Homological Algebra","author":"CA Weible","year":"1994","unstructured":"Weible, C.A.: An Introduction to Homological Algebra. Cambridge Studies in Advanced Mathematics, vol. 38. Cambridge University Press, Cambridge (1994)"},{"key":"9613_CR32","doi-asserted-by":"publisher","first-page":"3205","DOI":"10.1515\/forum-2013-6014","volume":"27","author":"X Yang","year":"2015","unstructured":"Yang, X., Ding, N.: On a question of Gillespie. Forum Math. 27, 3205\u20133231 (2015)","journal-title":"Forum Math."}],"container-title":["Applied Categorical Structures"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10485-020-09613-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10485-020-09613-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10485-020-09613-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,10]],"date-time":"2023-10-10T14:39:11Z","timestamp":1696948751000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10485-020-09613-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,24]]},"references-count":32,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2021,4]]}},"alternative-id":["9613"],"URL":"https:\/\/doi.org\/10.1007\/s10485-020-09613-x","relation":{},"ISSN":["0927-2852","1572-9095"],"issn-type":[{"value":"0927-2852","type":"print"},{"value":"1572-9095","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,10,24]]},"assertion":[{"value":"13 October 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 October 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 October 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}