Global $F$-regularity of Schubert varieties with applications to $\mathcal {D}$-modules

DOI10.1090/S0894-0347-05-00509-6zbMath1098.14038arXivmath/0402052OpenAlexW2137128294MaRDI QIDQ3376939

Jesper Funch Thomsen, Ulf Raben-Pedersen, Niels Lauritzen

Publication date: 27 March 2006

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0402052

zbMATH Keywords

Bruhat cellSchubert varietiesflag varietyVerma moduleglobally \(F\)-regulardeterminantal variety\(\mathcal D\)-modulestrongly \(F\)-regular\(F\)-regular\(F\)-rational

Mathematics Subject Classification ID

Grassmannians, Schubert varieties, flag manifolds (14M15) Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials (14F10) Local cohomology and algebraic geometry (14B15)

Related Items (15)

Perverse \(\mathbb{F}_p\)-sheaves on the affine Grassmannian ⋮ $F$-singularities: applications of characteristic $p$ methods to singularity theory ⋮ Another proof of the global \(F\)-regularity of Schubert varieties ⋮ On Frobenius splitting of orbit closures of spherical subgroups in flag varieties ⋮ On the collapsing of homogeneous bundles in arbitrary characteristic ⋮ Cohomology and geometry of Deligne-Lusztig varieties for \(\mathrm{GL}_n\) ⋮ Globally F-regular type of moduli spaces ⋮ Geometry of \(B\times B\)-orbit closures in equivariant embeddings ⋮ Schubert varieties are log Fano over the integers ⋮ Derived splinters in positive characteristic ⋮ Globally \(F\)-regular and log Fano varieties ⋮ Centers of \(F\)-purity ⋮ Log-terminal singularities and vanishing theorems via non-standard tight closure ⋮ On the \(F\)-rationality and cohomological properties of matrix Schubert varieties ⋮ Kollár's injectivity theorem for globally \(F\)-regular varieties

Cites Work

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• Dimension projective finie et cohomologie locale. Applications à la demonstration de conjectures de M. Auslander, H. Bass et A. Grothendieck
• Frobenius splitting and cohomology vanishing for Schubert varieties
• Equations defining Schubert varieties and Frobenius splitting of diagonals
• Kazhdan-Lusztig conjecture and holonomic systems
• Representations of Coxeter groups and Hecke algebras
• The intersection homology \(D\)-module in finite characteristic
• Local cohomology and \(\mathcal D\)-affinity in positive characteristic
• An analogue of holonomic \(D\)-modules on smooth varieties in positive characteristics
• Some results on \({\mathcal D}\)-modules on Borel varieties in characteristic \(p>0\)
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas (Quatrième partie). Rédigé avec la colloboration de J. Dieudonné
• Algebraic De Rham cohomology
• Tight closure and strong F-regularity
• Degeneracy Schemes and Schubert Varieties
• Line bundles on Bott-Samelson varieties
• Linear algebraic groups.
• Globally F-regular varieties: Applications to vanishing theorems for quotients of Fano varieties

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