The -cohomology in the semistable case

2019/09/09 by Kęstutis Česnavičius, Teruhisa Koshikawa
Mathematics · #advanced mathematical theories #Algebraic Geometry and Number Theory #Geometry and complex manifolds

paper · doi:10.1112/s0010437x1800790x

Abstract

For a proper, smooth scheme X over a p -adic field K , we show that any proper, flat, semistable O_K -model X of X whose logarithmic de Rham cohomology is torsion free determines the same O_K -lattice inside H_dRⁱ(X/K) and, moreover, that this lattice is functorial in X . For this, we extend the results of Bhatt–Morrow–Scholze on the construction and the analysis of an A_inf -valued cohomology theory of p -adic formal, proper, smooth O_K -schemes \mathfrakX to the semistable case. The relation of the A_inf -cohomology to the p -adic étale and the logarithmic crystalline cohomologies allows us to reprove the semistable conjecture of Fontaine–Jannsen.

Related

• p-adic derived de Rham cohomology
• A p-adic Cartier isomorphism between the A_inf-cohomology and de Rham-Witt complexes for semistable formal schemes
• Logarithmic A_{\rm inf}-cohomology
• Comparison of prismatic cohomology and derived de Rham cohomology
• Conjecture de l'inertie modérée de Serre