Dave Benson, in [2], conjectured that for any finite group G and any prime p the Castelnuovo-Mumford regularity of the cohomology ring, H(G,Fp), is zero. He showed that reg(H(G,Fp)) ≥ 0 and succeeded in proving equality when the difference between the dimension and the depth is at most two. The purpose of this paper is to prove Benson’s Regularity Conjecture as a corollary of the following result.

Let S be a standard N k-graded polynomial ring over a field K, let I be a multigraded homogeneous ideal of S, and let M be a finitely generated Z k-graded S-module. We prove that the resolution regularity, a multigraded variant of Castelnuovo-Mumford regularity, of I n M is asymptotically a linear function. This shows that the well known Z-graded phenomenon carries to multigraded situation.

S OF SOME OF MY PAPERS GROUPED BY TOPIC 1. Regularity. Let k be an algebraically closed field. We will work over a standard graded polynomial ring U over k. Projective dimension and regularity are the main numerical invariants that measure the complexity of a minimal free resolution. Let L be a homogeneous ideal in U , and let b ij (L) be its graded Betti numbers. The projective dimension pd(L)...

Here we define the concept of L-regularity for coherent sheaves on the Grassmannian G(1, 4) as a generalization of Castelnuovo-Mumford regularity on Pn. In this setting we prove analogs of some classical properties. We use our notion of L-regularity in order to prove a splitting criterion for rank 2 vector bundles with only a finite number of vanishing conditions. In the second part we give the...

Abstract Let $$A=\{a_0,\ldots ,a_{n-1}\}$$ A = { a 0 , … n - 1 } be a finite set of $$n\ge 4$$...