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1. Perfectoid pure singularities
   2024/09/26 by Bhargav Bhatt, Linquan Ma, Bhatt, Bhargav +11 · 4 citations
   Mathematics · #11G25 #13A35 #14B05 #14F18 #14G45 #Advanced Differential Equations and Dynamical Systems #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Number Theory (math.NT) #Rings, Modules, and Algebras
2. Test ideals in mixed characteristic: a unified theory up to perturbation
   2024/01/01 by Bhatt, Bhargav, Ma, Linquan, Patakfalvi, Zsolt +5 · 3 citations
   #13A35 #14F18 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics
3. Perfectoid signature, perfectoid Hilbert-Kunz multiplicity, and an application to local fundamental groups
   2022/09/08 by Cai, Hanlin, Lee, Seungsu, Ma, Linquan +2 · 3 citations
   #11G99 #13A35 #13C20 #13D22 #14B05 #14C20 #14D10 #14F18 #14F35 #14G45 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Number Theory (math.NT)
4. Deformations of log terminal and semi log canonical singularities
   2022/04/09 by Kenta Sato, Sato, Kenta, Shunsuke Takagi +1 · 1 citation
   Mathematics · #14B05 #14B07 #14F18 #14J17 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Geometry and complex manifolds
5. Logarithmic bounds on Fujita's conjecture
   2021/07/25 by Luca Ghidelli, Ghidelli, Luca, Justin Lacini +1 · 1 citation
   Mathematics · #14B05 #14C20 #14E05 #14F18 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Tensor decomposition and applications
6. Global generation of test ideals in mixed characteristic and applications
   2021/06/27 by Hacon, Christopher, Lamarche, Alicia, Schwede, Karl · 3 citations
   #13A35 #14B05 #14C20 #14F17 #14F18 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics
7. Arithmetic and geometric deformations of F-pure and F-regular singularities
   2021/03/05 by Kenta Sato, Sato, Kenta, Shunsuke Takagi +1 · 2 citations
   Mathematics · #13A35 #14B05 #14B07 #14D10 #14F18 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics
8. Hilbert-Kunz Multiplicity of Fibers and Bertini Theorems
   2019/08/13 by Datta, Rankeya, Simpson, Austyn · 2 citations
   #13A35 #14B05 #14F18 #14J17 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics
9. Geometric flow, Multiplier ideal sheaves and Optimal destabilizer for a Fano manifold
   2019/01/24 by Hisamoto, Tomoyuki · 1 citation
   #14F18 #32Q26 #53C44 #53C55 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics
10. Singularities in mixed characteristic via perfectoid big Cohen-Macaulay algebras
    2018/06/25 by Ma, Linquan, Schwede, Karl · 5 citations
    #11G99 #13A35 #13D22 #14B05 #14D10 #14F18 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics
11. Higher Lelong numbers and convex geometry
    2018/03/21 by Kim, Dano, Rashkovskii, Alexander · 1 citation
    #14F18 #32U05 #32U25 #52A39 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics #Metric Geometry (math.MG)
12. Versions of injectivity and extension theorems
    2014/06/24 by Gongyo, Yoshinori, Matsumura, Shin-ichi · 2 citations
    #14E30 #14F18 #32L10 #32L20 #Algebraic Geometry (math.AG) #Complex Variables (math.CV) #FOS: Mathematics
13. Modules of square integrable holomorphic germs
    2014/04/01 by László Lempert, Lempert, Laszlo · 1 citation
    Mathematics · #14F18 #32C35 #32L20 #32U05 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds
14. The weak ordinarity conjecture and F-singularities
    2013/07/14 by Bhatt, Bhargav, Schwede, Karl, Takagi, Shunsuke · 1 citation
    #13A35 #14B05 #14F18 #14F20 #14J17 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics
15. F-singularities in families
    2013/05/07 by Patakfalvi, Zsolt, Schwede, Karl, Zhang, Wenliang · 1 citation
    #13A35 #13B40 #14B05 #14D05 #14F18 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics
16. An algebraic approach to the openness conjecture of Demailly and Kollar
    2012/05/18 by Jonsson, Mattias, Mustata, Mircea · 1 citation
    #12J20 #14B05 (Secondary) #14F18 #32U05 (Primary) 32U25 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Complex Variables (math.CV) #FOS: Mathematics
17. Du Bois singularities deform
    2011/07/12 by Kovács, Sándor J, Schwede, Karl · 1 citation
    #14B05 #14B07 #14F17 #14F18 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics
18. Local positivity, multiplier ideals, and syzygies of abelian varieties
    2010/03/23 by Lazarsfeld, Robert, Pareschi, Giuseppe, Popa, Mihnea · 1 citation
    #14F18 #14K05 #Algebraic Geometry (math.AG) #FOS: Mathematics