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Article Dans Une Revue Transactions of the American Mathematical Society Année : 2022

SHEAVES OF E-INFINITY ALGEBRAS AND APPLICATIONS TO ALGEBRAIC VARIETIES AND SINGULAR SPACES

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Résumé

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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hal-03578199 , version 1 (17-02-2022)

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David Chataur, Joana Cirici. SHEAVES OF E-INFINITY ALGEBRAS AND APPLICATIONS TO ALGEBRAIC VARIETIES AND SINGULAR SPACES. Transactions of the American Mathematical Society, 2022, 375 (2), pp.925-960. ⟨10.1090/tran/8569⟩. ⟨hal-03578199⟩
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