Algebraic geometry in mixed characteristic
DOI10.4171/icm2022/113arXiv2112.12010OpenAlexW4389775204MaRDI QIDQ6118166
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Publication date: 20 March 2024
Published in: International Congress of Mathematicians (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2112.12010
algebraic \(K\)-theorytopological Hochschild homologyRiemann-Hilbert correspondenceminimal model programvanishing theorems\(p\)-adic Hodge theoryprismatic cohomology
Vanishing theorems in algebraic geometry (14F17) Research exposition (monographs, survey articles) pertaining to algebraic geometry (14-02) Varieties over finite and local fields (11G25) (p)-adic cohomology, crystalline cohomology (14F30) Homological methods in commutative ring theory (13D99) (K)-theory of local fields (11S70) (K)-theory in number theory (19F99) Perfectoid spaces and mixed characteristic (14G45)
Cites Work
- A canonical linear system associated to adjoint divisors in characteristic \(p>0\)
- Rigidity and a Riemann-Hilbert correspondence for \(p\)-adic local systems
- Syntomic complexes and \(p\)-adic nearby cycles
- Existence of Mori fibre spaces for 3-folds in char \(p\)
- Homotopical algebraic geometry. I: Topos theory
- The basic geometry of Witt vectors. I: The affine case
- A Riemann-Hilbert correspondence in positive characteristic
- Motivic cohomology over Dedekind rings
- On certain types of \(p\)-adic representations of the Galois group of a local field; construction of a Barsott-Tate ring.
- Absolute integral closure in positive characteristic
- Nonabelian Hodge theory in characteristic \(p\)
- On the K-theory of algebraically closed fields
- Higher direct images of dualizing sheaves. I
- Higher direct images of dualizing sheaves. II
- Algebraic cycles and higher K-theory
- \(p\)-adic étale cohomology
- Relèvements modulo \(p^ 2\) et décomposition du complexe de de Rham. (Lifting modulo \(p^ 2\) and decomposition of the de Rham complex)
- Splitting in integral extensions, Cohen-Macaulay modules and algebras
- Continuous cohomology and \(p\)-adic Galois representations
- Infinite integral extensions and big Cohen-Macaulay algebras
- Milnor \(K\)-theory is the simplest part of algebraic \(K\)-theory
- Higgs bundles and local systems
- Algebraic K-theory and crystalline cohomology
- Basepoint freeness for nef and big line bundles in positive characteristic
- Semi-stable representations and strongly divisible modules
- \(p\)-adic étale cohomology and crystalline cohomology in the semi-stable reduction case
- Cyclic polytopes and the \(K\)-theory of truncated polynomial algebras
- The Hodge filtration and cyclic homology
- Arithmetic analogues of derivations
- Almost ring theory
- On the \(K\)-theory of local fields
- Big Cohen-Macaulay algebras and the vanishing conjecture for maps of Tor in mixed characteristic
- Integral perfectoid big Cohen-Macaulay algebras via André's theorem
- On the direct summand conjecture and its derived variant
- A finer Tate duality theorem for local Galois symbols
- Abhyankar's perfectoid lemma
- The direct factor conjecture
- The vanishing conjecture for maps of Tor and derived splinters
- On topological cyclic homology
- Integral \(p\)-adic Hodge theory
- Total \(p\)-differentials on schemes over \(\mathbb Z/p^{2}\)
- A \(p\)-adic Simpson correspondence. II: Small representations
- The cyclotomic trace and algebraic K-theory of spaces
- The direct summand conjecture in dimension three.
- Big Cohen-Macaulay algebras in dimension three via Heitmann's theorem.
- On the \(K\)-theory of finite algebras over Witt vectors of perfect fields
- Perfectoid spaces
- The \(K\)-theory of fields in characteristic \(p\)
- Perfectoid multiplier/test ideals in regular rings and bounds on symbolic powers
- Integral \(p\)-adic Hodge theory of formal schemes in low ramification
- Integral \(p\)-adic étale cohomology of Drinfeld symmetric spaces
- The \(\operatorname{arc}\)-topology
- Remarks on \(K(1)\)-local \(K\)-theory
- Periodic cyclic homology and derived de Rham cohomology
- On \(q\)-de Rham cohomology via \(\Lambda \)-rings
- From algebraic cobordism to motivic cohomology
- Homological conjectures, old and new
- Projectivity of the Witt vector affine Grassmannian
- Topological Hochschild homology and integral \(p\)-adic Hodge theory
- Working session: Topological cyclic homology. Abstracts from the working session held April 1--7, 2018
- On the crystalline period map
- \(p\)-adic deformation of algebraic cycle classes
- Complexe cotangent et déformations. I. (The cotangent complex and deformations. I.)
- Complexe cotangent et déformations. II
- Equations différentielles à points singuliers réguliers
- A \(p\)-adic Simpson correspondence
- A note on lattices in semi-stable representations
- The p-adic Simpson Correspondence
- Existence of flips and minimal models for 3-folds in char $p$
- $p$-adic periods and derived de Rham cohomology
- The pro-\'etale topology for schemes
- On relative and bi-relative algebraic 𝐾-theory of rings of finite characteristic
- Absolute Integral Closure
- Logarithmic geometry and algebraic stacks
- Revisiting the de Rham-Witt complex
- Tight Closure, Invariant Theory, and the Briancon-Skoda Theorem
- Milnor 𝐾-theory of local rings with finite residue fields
- Algebraic $K$-theory and etale cohomology
- Complexe de de\thinspace Rham-Witt et cohomologie cristalline
- Complexe de de Rham filtré d'une variété singulière
- Logarithmic structures of Fontaine-Illusie. II
- Higher algebraic K-theory: I
- Duality in the flat cohomology of a surface
- Notes on Crystalline Cohomology. (MN-21)
- Crystalline conjecture via K-theory
- Integral crystalline cohomology over very ramified valuation rings
- Semistable Minimal Models of Threefolds in Positive or Mixed Characteristic
- Minimal model program for excellent surfaces
- $F$-singularities: applications of characteristic $p$ methods to singularity theory
- Canonical<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>q</mml:mi></mml:math>-deformations in arithmetic geometry
- ℚ-Gorenstein splinter rings of characteristic p are F-regular
- p-Adic Hodge Theory
- HOMOLOGY OF THE FULL LINEAR GROUP OVER A LOCAL RING, AND MILNOR'SK-THEORY
- The spectral sequence relating algebraic K-theory to motivic cohomology
- Derived splinters in positive characteristic
- Topological Hochschild homology of number rings
- 𝐾-theory and topological cyclic homology of henselian pairs
- Notes on the $$\mathbb A_{{\mathrm {inf}}}$$-Cohomology of Integral p-Adic Hodge Theory
- p-ADIC GEOMETRY
- Specializing varieties and their cohomology from characteristic 0 to characteristic 𝑝
- The -cohomology in the semistable case
- Weak functoriality of Cohen-Macaulay algebras
- An Invitation to Gabor Analysis
- F-singularities via alterations
- On the three dimensional minimal model program in positive characteristic
- Stabilization of the cohomology of thickenings
- Homotopical algebraic geometry. II. Geometric stacks and applications
- p-adic étale Tate twists and arithmetic duality☆
- Mixed Hodge Structures
- Crystalline representations and F-crystals
- Potentially semi-stable deformation rings
- The homotopy coniveau tower
- Characterizations of Regular Local Rings of Characteristic p
- The de Rham-Witt complex and 𝑝-adic vanishing cycles
- Mixed Hodge modules
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