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We demonstrate that the topological Helly theorem and the algebraicAuslander-Buchsbaum may be viewed as different versions of the same phenomenon.Using this correspondence we show how the colorful Helly theorem of I.Baranyand its generalizations by G.Kalai and R.Meshulam translates to the algebraicside. Our main results are algebraic generalizations of these translations,which in particular gives a syzygetic version of Hellys theorem.

The colorful Helly theorem and colorful resolutions of ideals