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http://hdl.handle.net/2445/190227
Title: | Sheaves of E-infinity algebras and applications to algebraic varieties and singular spaces |
Author: | Chataur, David Cirici, Joana |
Keywords: | Topologia algebraica Homologia Teoria de Hodge Algebraic topology Homology Hodge theory |
Issue Date: | 2022 |
Publisher: | American Mathematical Society (AMS) |
Abstract: | 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. |
Note: | Versió postprint del document publicat a: https://doi.org/10.1090/tran/8569 |
It is part of: | Transactions of the American Mathematical Society, 2022, vol. 375, num. 2, p. 925-960 |
URI: | http://hdl.handle.net/2445/190227 |
Related resource: | https://doi.org/10.1090/tran/8569 |
ISSN: | 0002-9947 |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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