2024/02/27 by Gleb Terentiuk, Vadim Vologodsky, Terentiuk, Gleb +3
Mathematics · #Rings, Modules, and Algebras #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models
paper · pdf · doi:10.1017/s0010437x26102978
ABSTRACT Let k be a perfect field of characteristic p and let W ( k ) be its ring of Witt vectors. We construct an equivalence of categories between the full subcategory of the derived category of quasi-coherent sheaves on the syntomification of W ( k ) spanned by objects whose Hodge–Tate weights are between left bracket 0 comma p minus 2 right bracket <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mo stretchy="false">[</mml:mo> <mml:mn>0</mml:mn> <mml:mo>,</mml:mo> <mml:mi>p</mml:mi> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> <mml:mo stretchy="false">]</mml:mo> </mml:math> [0,p-2] and an appropriate derived category of Fontaine–Laffaille modules.