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Explore a comprehensive lecture on the generalization of torsion vanishing results for the cohomology of general Shimura varieties of PEL type A or C. Delve into the combination of Koshikawa's technique, geometric Eisenstein series theory over the Fargues-Fontaine curve, and Santos' work on the Hodge-Tate period morphism. Examine the comparison of Hecke correspondences on G-bundles moduli stack with Shimura varieties cohomology. Discover a new description of generic cohomology parts and a novel filtration on compactly supported cohomology. Investigate the relationship between torsion cohomology behavior and Hecke eigensheaves perversity under the spectral Bernstein center action. Consider new conjectures on torsion cohomology structure and their implications for future research in this field.
