Lattices in potentially semi-stable representations and weak (φ,G)-modules

2015/02/02 by Yoshiyasu Ozeki, Ozeki, Yoshiyasu · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1502.00340

arxiv created 2015/02/02 · openalex publication_date 2015/02/02 · arxiv updated 2015/02/03 · openalex created_date 2016/08/23 · openalex updated_date 2026/07/28

Abstract

Let p be a prime number and r a non-negative integer. In this paper, we prove that there exists an anti-equivalence between the category of weak (φ,G)-modules of height r and a certain subcategory of the category of Galois stable lattices in potentially semi-stable p-adic representations with Hodge-Tate weights in [0,r]. This gives an answer to a Tong Liu's question about the essential image of a functor on weak (φ,G)-modules. For a proof, following Liu's methods, we construct linear algebraic data which classify lattices in potentially semi-stable representations.

Citations

• Compatibility of Kisin modules for different uniformizers

Cited by

• Potential semistability of Finite height Galois representations: Relative case

Related

• Galois Lattices and Strongly Divisible Lattices in the Unipotent Case
• A note on lattices in semi-stable representations
• Reduction modulo p of certain semi-stable representations
• Torsion representations arising from (φ,G)-modules
• Regular filtered (phi,N)-modules of dimension 3