Abstract
We prove that the algebra of closed differential forms on an (algebraic, formal, or analytic) disk with logarithmic singularities along several coordinate hyperplanes is Koszul (both nontopologically and topologically). A relation to variations of mixed Hodge-Tate structures is discussed in the introduction.
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 46, No. 3, pp. 71–80, 2012
|Original Russian Text Copyright © by L. E. Positselski
This work was supported by E. Balzan’s prize in mathematics won by P. Deligne in 2004, the Simons foundation, and RFBR grants nos. 10-01-93113-NTsNIL a, 11-01-00393-a, and 11-01-12072-ofi-m-2011.
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Positselski, L.E. Closed form algebra on a disk is Koszul. Funct Anal Its Appl 46, 218–224 (2012). https://doi.org/10.1007/s10688-012-0027-z
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DOI: https://doi.org/10.1007/s10688-012-0027-z