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In this paper, we prove that for the oper stratification of the de Rham moduli space $M_{mathrm{dR}}(X,r)$, the closed oper stratum is the unique minimal stratum with dimension $r^2(g-1)+g+1$, and the open dense stratum consisting of irreducible flat bundles with stable underlying vector bundles is the unique maximal stratum.
For an abeloid variety $A$ over a complete algebraically closed field extension $K$ of $mathbb Q_p$, we construct a $p$-adic Corlette-Simpson correspondence, namely an equivalence between finite-dimensional continuous $K$-linear representations of th
We show that the Friedlander-Mazur conjecture holds for a sequence of products of projective varieties such as the product of a smooth projective curve and a smooth projective surface, the product of two smooth projective surfaces, the product of arb
Using the work of Guillen and Navarro Aznar we associate to each real algebraic variety a filtered chain complex, the weight complex, which is well-defined up to filtered quasi-isomorphism, and which induces on Borel-Moore homology with Z/2 coefficie
The classical additive Deligne-Simpson problem is the existence problem for Fuchsian connections with residues at the singular points in specified adjoint orbits. Crawley-Boevey found the solution in 2003 by reinterpreting the problem in terms of qui
We study the Hodge filtration on the local cohomology sheaves of a smooth complex algebraic variety along a closed subscheme Z in terms of log resolutions, and derive applications regarding the local cohomological dimension, the Du Bois complex, loca