On de Jong's conjecture

DOI10.1007/s11856-006-0006-2zbMath1123.11020arXivmath/0402184OpenAlexW2073566464WikidataQ122861156 ScholiaQ122861156MaRDI QIDQ877470

Dennis Gaitsgory

Publication date: 23 April 2007

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0402184

zbMATH Keywords

stacksderived categoriesfundamental groupsGalois representationsHecke operatorscurves over finite fieldsLanglands conjecturespecial sheaves

Mathematics Subject Classification ID

Arithmetic ground fields for curves (14H25) Curves over finite and local fields (11G20) Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials (14F10) Coverings of curves, fundamental group (14H30) Galois representations (11F80) Homotopy theory and fundamental groups in algebraic geometry (14F35) Hecke-Petersson operators, differential operators (one variable) (11F25) Langlands-Weil conjectures, nonabelian class field theory (11R39) Generalizations (algebraic spaces, stacks) (14A20)

Related Items

On parabolic restriction of perverse sheaves, Compatible intertwiners for representations of finite nilpotent groups, Geometric Langlands for hypergeometric sheaves, Twisted geometric Satake equivalence via gerbes on the factorizable grassmannian, Vanishing theorems for perverse sheaves on abelian varieties, revisited, Airy sheaves for reductive groups, Arithmetic and geometric Langlands program, Cohomology of semisimple local systems and the decomposition theorem, Kloosterman sheaves for reductive groups, Cuspidal cohomology of stacks of shtukas, Integrality of the Betti moduli space, On the pro-semisimple completion of the fundamental group of a smooth variety over a finite field, The test function conjecture for local models of Weil-restricted groups, Motives with exceptional Galois groups and the inverse Galois problem, Geometric Weil representation in characteristic two, Chtoucas pour les groupes réductifs et paramétrisation de Langlands globale, Picard-Lefschetz oscillators for the Drinfeld-Lafforgue-Vinberg degeneration for \(\mathrm{SL}_2\), Deformations and the rigidity method, Serre's conjecture and its consequences, Problems in arithmetic topology, Unit interval orders and the dot action on the cohomology of regular semisimple Hessenberg varieties, Chiral principal series categories. I: Finite dimensional calculations, Epipelagic representations and rigid local systems, Characteristic classes and Hilbert-Poincaré series for perverse sheaves on abelian varieties, The motivic Satake equivalence, Spectral action in Betti geometric Langlands, On the semisimplicity of reductions and adelic openness for 𝐸-rational compatible systems over global function fields, Mod \(\ell\) representations of arithmetic fundamental groups. I: An analog of Serre's conjecture for function fields, Vanishing theorems for constructible sheaves on abelian varieties, Lifting and automorphy of reducible mod \(p\) Galois representations over global fields

Cites Work

• Unnamed Item
• Unnamed Item
• On a vanishing conjecture appearing in the geometric Langlands correspondence
• Geometric Langlands duality and representations of algebraic groups over commutative rings
• On the geometric Langlands conjecture
• Grothendieck topologies and deformation theory II
• A conjecture on arithmetic fundamental groups
• Construction of central elements in the affine Hecke algebra via nearby cycles