Proves Dolbeault geometric Langlands equivalence for GL_r and SL_r/PGL_r over the locus of spectral curves with at worst type A singularities, extending beyond the elliptic locus via Whittaker normalization.
Proof of the geometric Langlands conjecture II: Kac- Moody localization and the FLE.arXiv:2405.03648
4 Pith papers cite this work. Polarity classification is still indexing.
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Proves homological mirror symmetry equivalence between Fukaya categories of generic-microlocal-monodromy moduli and coherent sheaves on minimal resolutions of trivial-microlocal-monodromy moduli for rank-two local systems on the projective line.
Constructs semiorthogonal decompositions for derived categories on quasi-smooth derived algebraic stacks indexed by component lattices, with examples for moduli stacks of G-bundles, G-Higgs bundles, and G-local systems.
Constructs the quantum geometric Langlands functor in the Betti setting via Whittaker coefficients and proves compatibility with the 2-Fourier-Mukai equivalence between sheaves of categories over 2-stacks Ge_{Z_G} and Ge_{π_1(Ĝ)}.
citing papers explorer
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The Dolbeault geometric Langlands correspondence for type A groups beyond the elliptic locus
Proves Dolbeault geometric Langlands equivalence for GL_r and SL_r/PGL_r over the locus of spectral curves with at worst type A singularities, extending beyond the elliptic locus via Whittaker normalization.
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Semiorthogonal decompositions for stacks
Constructs semiorthogonal decompositions for derived categories on quasi-smooth derived algebraic stacks indexed by component lattices, with examples for moduli stacks of G-bundles, G-Higgs bundles, and G-local systems.