W. Frank Moore

Connected sums of Gorenstein local rings

Abstract Given surjective homomorphisms R → T ← S of local rings, and ideals in R and S that are isomorphic to some T-module V, the connected sum R⋕TS is defined to be the ring obtained by factoring out the diagonal image of V in the fiber product R ×TS. When T is Cohen–Macaulay of dimension d and V is a canonical module of T, it is proved that if R and S are Gorenstein of dimension d, then so is R⋕TS. This result is used to study how closely an artinian ring can be approximated by a Gorenstein ring mapping onto it. When T is regular, it is shown that R⋕TS almost never is a complete intersection ring. The proof uses a presentation of the cohomology algebra as an amalgam of the algebras and over isomorphic polynomial subalgebras generated by one element of degree 2.

On the discriminant of twisted tensor products

Abstract We provide formulas for computing the discriminant of noncommutative algebras over central subalgebras in the case of Ore extensions and skew group extensions. The formulas follow from a more general result regarding the discriminants of certain twisted tensor products. We employ our formulas to compute automorphism groups for examples in each case.

Moment angle complexes and big Cohen–Macaulayness

Let ZK C m be the moment angle complex associated to a simplicial complex K on amc, together with the natural action of the torus TD U.1/ m . Let G T be a (possibly disconnected) closed subgroup and RWD T=G. Let ZaKc be the Stanley‐ Reisner ring of K and consider ZaR cWD H .BRIZ/ as a subring of ZaT cWD H .BTIZ/. We prove that H G .ZKIZ/ is isomorphic to Tor ZaR c .ZaKc;Z/ as a graded module over ZaT c. Based on this, we characterize the surjectivity of H T .ZKIZ/! H G .ZKIZ/ (ie H odd G .ZKIZ/D 0) in terms of the vanishing of Tor ZaR c 1 .ZaKc;Z/ and discuss its relation to the freeness and the torsion-freeness of ZaKc over ZaR c. For various toric orbifolds X , by which we mean quasitoric orbifolds or toric Deligne‐Mumford stacks, the cohomology of X can be identified with H G.ZK/ with appropriate K and G and the above results mean that H .XIZ/a Tor ZaR c.ZaKc;Z/ and that H odd .XIZ/D0 if and only if H .XIZ/ is the quotient H R.XIZ/. 55N91; 57R18, 53D20, 14M25

Auslander’s theorem for permutation actions on noncommutative algebras

When

CONNECTED SUMS OF SIMPLICIAL COMPLEXES AND EQUIVARIANT COHOMOLOGY

A = \mathbb{k}[x_1, \ldots, x_n]

The vanishing of a higher codimension analogue of Hochster’s theta invariant

and

Periodic free resolutions from twisted matrix factorizations

G

Finiteness conditions on the Yoneda algebra of a monomial algebra

is a small subgroup of

Cohomology of Fiber Products of Local Rings

\operatorname{GL}_n(\mathbb{k})

Noncommutative Kn\"{o}rrer periodicity and noncommutative Kleinian singularities

, Auslanders Theorem says that the skew group algebra