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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/190227
Sheaves of E-infinity algebras and applications to algebraic varieties and singular spaces
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ABSTRACT. We describe the $E$-infinity algebra structure on the complex of singular cochains of a topological space, in the context of sheaf theory. As a first application, for any algebraic variety we define a weight filtration compatible with its $E$-infinity structure. This naturally extends the theory of mixed Hodge structures in rational homotopy to $p$-adic homotopy theory. The spectral sequence associated to the weight filtration gives a new family of algebraic invariants of the varieties for any coefficient ring, carrying Steenrod operations. As a second application, we promote Deligne's intersection complex computing intersection cohomology, to a sheaf carrying E-infinity structures. This allows for a natural interpretation of the Steenrod operations defined on the intersection cohomology of any topological pseudomanifold.
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CHATAUR, David and CIRICI, Joana. Sheaves of E-infinity algebras and applications to algebraic varieties and singular spaces. Transactions of the American Mathematical Society. 2022. Vol. 375, num. 2, pags. 925-960. ISSN 0002-9947. [consulted: 9 of October of 2026]. Available at: https://hdl.handle.net/2445/190227