Logarithmic Hochschild homology is functorial for strong log Fourier-Mukai transforms on smooth proper log pairs, yielding a dg bicategory of logarithmic correspondences with compatible Chern characters and Euler pairings.
Proper local complete intersection morphisms preserve perfect complexes
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Let $f : X \longrightarrow Y$ be a proper and local complete intersection morphism of schemes. We prove that $\mathbb{R}f_{*}$ preserves perfect complexes, without any projectivity or noetherian assumptions. This provides a different proof of a theorem by Neeman and Lipman based on techniques from derived algebraic geometry to proceed a reduction to the noetherian case.
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Constructs a flat degeneration of the Higgs bundle moduli stack on curves with intrinsic log-symplectic form, flat Hitchin map with complete fibers, and Lagrangian nilpotent cone locus, extended over stable curves.
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Functoriality of logarithmic Hochschild homology of log smooth pairs
Logarithmic Hochschild homology is functorial for strong log Fourier-Mukai transforms on smooth proper log pairs, yielding a dg bicategory of logarithmic correspondences with compatible Chern characters and Euler pairings.
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Moduli stacks of Higgs bundles on stable curves
Constructs a flat degeneration of the Higgs bundle moduli stack on curves with intrinsic log-symplectic form, flat Hitchin map with complete fibers, and Lagrangian nilpotent cone locus, extended over stable curves.