The p-adic Simpson Correspondence II: Functoriality by proper direct image and Hodge-Tate local systems -- an overview - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2022

The p-adic Simpson Correspondence II: Functoriality by proper direct image and Hodge-Tate local systems -- an overview

Résumé

Faltings initiated in 2005 a p-adic analogue of the (complex) Simpson correspondence whose construction has been taken up by various authors, according to several approaches. Following the one we initiated previously, we present an overview of a new monograph developing new features of the p-adic Simpson correspondence, inspired by our construction of the relative Hodge-Tate spectral sequence. First, we address the connection to Hodge-Tate local systems. Second, we establish the functoriality of the p-adic Simpson correspondence by proper direct image. Along the way, we expand the scope of our original construction.

Dates et versions

hal-03822555 , version 1 (20-10-2022)

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Ahmed Abbes, Michel Gros. The p-adic Simpson Correspondence II: Functoriality by proper direct image and Hodge-Tate local systems -- an overview. 2022. ⟨hal-03822555⟩
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