Hodge theory of $p$-adic varieties: a survey

DOI10.4064/ap200516-31-8zbMath1483.11130arXiv2005.07919OpenAlexW3112651723MaRDI QIDQ5028961

Wiesława Nizioł

Publication date: 11 February 2022

Published in: Annales Polonici Mathematici (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2005.07919

zbMATH Keywords

\(p\)-adic cohomologyanalytic varieties

Mathematics Subject Classification ID

Varieties over finite and local fields (11G25) Transcendental methods, Hodge theory (algebro-geometric aspects) (14C30)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Syntomic cohomology and \(p\)-adic regulators for varieties over \(p\)-adic fields
• Syntomic complexes and \(p\)-adic nearby cycles
• Completely continuous endomorphisms of \(p\)-adic Banach spaces
• Diophantine problems and \(p\)-adic period mappings
• On certain types of \(p\)-adic representations of the Galois group of a local field; construction of a Barsott-Tate ring.
• On uniqueness of \(p\)-adic period morphisms
• Finiteness theorems for abelian varieties over number fields.
• The proof of the Mordell conjecture
• There are no abelian varieties over \(\mathbb Z\).
• \(p\)-adic étale cohomology
• \(p\)-adic étale cohomology and crystalline cohomology in the semi-stable reduction case
• Cohomology of crystalline representations
• Almost \(C_p\)-representation
• \(p\)-adic representations and differential equations
• Hasse-Arf filtrations and \(p\)-adic monodromy.
• Analogue \(p\)-adique du théorème de Turrittin et le théorème de la monodromie \(p\)-adique.
• Derived Galois deformation rings
• Banach-Colmez spaces and coherent sheaves on the Fargues-Fontaine curve
• On topological cyclic homology
• Integral \(p\)-adic Hodge theory
• A \(p\)-adic local monodromy theorem
• A class of \(p\)-adic Galois representations arising from abelian varieties over \(\mathbb Q_p\)
• Modular elliptic curves and Fermat's Last Theorem
• Perfectoid spaces
• A construction of \(\mathbf B_{\text{dR}}^+\)
• The \(K\)-theory of fields in characteristic \(p\)
• Cohomology of \(p\)-adic Stein spaces
• Explicit Chabauty-Kim for the split Cartan modular curve of level 13
• On \(p\)-adic absolute Hodge cohomology and syntomic coefficients. I.
• Topological Hochschild homology and integral \(p\)-adic Hodge theory
• Rigid analytix \(p\)-divisible groups
• On the crystalline period map
• Semistable conjecture via \(K\)-theory
• Rigid analytic spaces
• The motivic fundamental group of \(\mathbf P^1\setminus\{0,1,\infty\}\) and the theorem of Siegel
• -ADIC HODGE THEORY FOR RIGID-ANALYTIC VARIETIES
• $p$-adic periods and derived de Rham cohomology
• Le programme de Langlands $p$-adique
• The Fontaine-Mazur conjecture for $ {GL}_2$
• GALOIS MODULI OF PERIOD $p$ GROUP SCHEMES OVER A RING OF WITT VECTORS
• Schémas en groupes de type $(p,\ldots,p)$
• Crystalline conjecture via K-theory
• Finiteness theorems for the cohomology of an overconvergent isocrystal on a curve
• ESPACES DE BANACH DE DIMENSION FINIE
• p-Adic Hodge Theory
• On p-adic comparison theorems for rigid analytic varieties, I
• On the Cohomology of the Affine Space
• The -cohomology in the semistable case
• Berkeley Lectures on p-adic Geometry
• Cohomologie 𝑝-adique de la tour de Drinfeld: le cas de la dimension 1
• Beilinson-Flach elements and Euler systems I: Syntomic regulators and 𝑝-adic Rankin 𝐿-series
• Relative p-adic Hodge theory: Foundations
• The de Rham-Witt complex and 𝑝-adic vanishing cycles