A Comment on the Positive Canons Project

Using the machinery of positive political theory in order to make some sense of legislative intent contains a number of provocative possibilities. Issues that require attention in this theory are addressed

Nonvanishing cohomology and classes of Gorenstein rings

We give counterexamples to the following conjecture of Auslander: given a finitely generated module $M$ over an Artin algebra $\Lambda$, there exists a positive integer $n_M$ such that for all finitely generated $\Lambda$-modules $N$, if \Ext_{\Lambda}^i(M,N)=0 for all $i\gg 0$, then \Ext_{\Lambda}^i(M,N)=0 for all $i\geq n_M$. Some of our examples moreover yield homologically defined classes of commutative local rings strictly between the class of local complete intersections and the class of local Gorenstein rings.Comment: 16 page

On the growth of the Betti sequence of the canonical module

We study the growth of the Betti sequence of the canonical module of a Cohen-Macaulay local ring. It is an open question whether this sequence grows exponentially whenever the ring is not Gorenstein. We answer the question of exponential growth affirmatively for a large class of rings, and prove that the growth is in general not extremal. As an application of growth, we give criteria for a Cohen-Macaulay ring possessing a canonical module to be Gorenstein.Comment: 12 pages. version 2: includes omitted author contact informatio