2 problems

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Kollár's package conjecture for the S-sheaf of an intersection complex
Let $\mathbb{V}$ be a variation of Hodge structure on a regular Zariski open subset of a projective variety $X$ , and let $S(IC_X(\mathbb{V}))$ denote Kollár's coherent S-sheaf asso…
Conjecturesolvedcoherent-sheaves mixed-hodge-modules variation-of-hodge-structurearXiv posted 2 days ago
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The Tannakian variation conjecture for graded cohomology of stable G-bundles
Tannakian variation conjecture. The variation of Hodge structure associated to $Gr_W H^i({\rm Bun}^s_{G,C})$ lies in the Tannakian subcategory generated by $R^1\pi_*{\mathbb Q}$ fo…
Conjectureopenmoduli-of-bundles tannakian-categories variation-of-hodge-structurearXiv posted 2 days ago

Kollár's package conjecture for the S-sheaf of an intersection complex