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Math.106, 611?638 (1984)",{"doi":600},"10.2307\u002F2374287",{"id":602,"createTime":603,"updateTime":604,"relativeEntities":605,"slug":606,"properties":607,"entityType":54,"verifyStatus":55,"verifyTime":604,"verifyNote":56,"languages":18,"translateLanguages":18,"viewCount":19,"primaryUrl":616,"fullTextUrl":617,"authors":618,"publicationType":132,"publisherRelationship":656,"citationCount":18,"citationInfo":18,"publishDate":670,"publishYear":671,"citationAnalyzeStatus":17,"lastCitationAnalyze":18,"indexDatabases":672,"openAccess":18,"references":18,"isForceReanalyzing":263},"ae8495fa-1ce1-4012-82b9-1314d9a6146f","2024-04-06T17:19:57.822+00:00","2024-10-26T06:51:54.724+00:00",[],"A-prismatic-approach-to-crystalline-local-systems",{"abstract":608,"title":610,"references":612,"doi":614},{"EN":609},"Let $X$ be a smooth $p$ -adic formal scheme. We show that integral crystalline local systems on the generic fiber of $X$ are equivalent to prismatic $F$ -crystals over the analytic locus of the prismatic site of $X$ . As an application, we give a prismatic proof of Fontaine’s $\\mathrm {C}_{{\\mathrm {crys}}}$ -conjecture, for general coefficients, in the relative setting, and allowing ramified base fields. Along the way, we also establish various foundational results for the cohomology of prismatic $F$ -crystals, including various comparison theorems, Poincaré duality, and Frobenius isogeny.",{"EN":611},"A prismatic approach to crystalline local systems",{"VOID":613},"citation_journal_title=Rend. Semin. Mat. Univ. Padova; citation_title=Semistable sheaves and comparison isomorphisms in the semistable case; citation_author=F. Andreatta, A. Iovita; citation_volume=128; citation_publication_date=2012; citation_pages=131-285; citation_id=CR1\ncitation_journal_title=J. Inst. Math. 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