Functional Analysis and Its Applications

, Volume 46, Issue 3, pp 218-224

First online:

Closed form algebra on a disk is Koszul

  • L. E. PositselskiAffiliated withFaculty of Mathematics and Laboratory of Algebraic Geometry of Higher School of Economics, Institute for Information Transmission Problems Email author 

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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.

Key words

closed differential form with logarithmic singularities mixed Hodge-Tate sheave Koszul algebra Koszul module quasi-algebra with external multiplication topological Koszulity