The algebra of closed forms in a disk is Koszul

Abstract

We prove that the algebra of closed differential forms in an (algebraic, formal, or analytic) disk with logarithmic singularities along several coordinate hyperplanes is (both nontopologically and topologically) Koszul. The connection with variations of mixed Hodge-Tate structures, based on a preprint by Andrey Levin, is discussed in the introduction.

arXiv commentLaTeX 2e, 9 pages; v.2: small additions in sections 1-2, correction in section 3; v.3: explanations concerning the connection with mixed Hodge-Tate sheaves added to the introduction, detalizations and correction in section 1; v.4: small details added here and there, major correction in section 3; v.5: one reference added

References in corpus (3)

• Koszul property and Bogomolov's conjecture
• Galois cohomology of a number field is Koszul
• Koszul duality and Galois cohomology