Related papers: Vanishing of Tor Over Complete Intersections

Gang, Kim and Yoon have recently proposed a conjecture on a vanishing identity of adjoint Reidemeister torsions of hyperbolic 3-manifolds with torus boundary, from the viewpoint of wrapped M5-branes. In this paper, we provide infinitely…

We develop a new approach to non-Hausdorff \'etale groupoids and their algebras based on Timmermann's construction of Hausdorff covers. As an application, we completely characterise when singular ideals vanish in Steinberg algebras over…

We show that symmetry in the vanishing of cohomology holds for graded modules over quantum complete intersections. Moreover, symmetry holds for all modules if the algebra is symmetric.

Conditions on the Koszul complex of a noetherian local ring $R$ guarantee that $\mathrm{Tor}^{R}_{i}(M,N)$ is non-zero for infinitely many $i$, when $M$ and $N$ are finitely generated $R$-modules of infinite projective dimension. These…

For a commutative Noetherian local ring we define and study the class of modules having reducible complexity, a class containing all modules of finite complete intersection dimension. Various properties of this class of modules are given,…

Let \fa be an ideal of a commutative Noetherian ring R and M and N two finitely generated R-modules. Let \cd_{\fa}(M,N) denote the supremum of the i's such that H^i_{\fa}(M,N)\neq 0. First, by using the theory of Gorenstein homological…

The absence of resistivity saturation in many strongly correlated metals, including the high-temperature superconductors, is critically examined from the viewpoint of optical conductivity measurements. Coherent quasiparticle conductivity,…

We construct a minimal projective bimodule resolution for every finite dimensional quantum complete intersection of codimension two. Then we use this resolution to compute both the Hochschild cohomology and homology for such an algebra. In…

Let $R$ be a commutative ring and $M$ be an $R$-module, and let $I(R)^*$ be the set of all non-trivial ideals of $R$. The $M$-intersection graph of ideals of $R$, denoted by $G_M(R)$, is a graph with the vertex set $I(R)^*$, and two…

Let $X$ be a general complete intersection of a given multi-degree in a complex projective space. Suppose that the anti-canonical line bundle of $X$ is ample. Using the cylinder homomorphism associated with the family of complete…

Let $\xx= x_1,\ldots,x_r$ denote a system of elements of a commutative ring $R$. For an $R$-module $M$ we investigate when $\xx$ is $M$-pro-regular resp. $M$-weakly pro-regular as generalizations of $M$-regular sequences. This is done in…

In \cite{Broer1993}, it was shown that certain line bundles on $\widetilde{\mathcal{N}}=T^*G/B$ have vanishing higher cohomology. We prove a generalization of this theorem for real reductive algebraic groups. More specifically, if…

We prove that each positive power of the maximal ideal of a commutative Noetherian local ring is Tor-rigid, and strongly-rigid. This gives new characterizations of regularity and, in particular, shows that such ideals satisfy the torsion…

We prove two theorems on the vanishing of Ext over commutative Noetherian local rings. Our first theorem shows that there are no Burch ideals which are rigid over non-regular local domains. Our second theorem reformulates a conjecture of…

We overview a web of conjectures about torsors under reductive groups over regular rings and survey some techniques that have been used for making progress on such problems.

The breakup of shearless invariant tori with winding number $\omega=[0,1,11,1,1,...]$ (in continued fraction representation) of the standard nontwist map is studied numerically using Greene's residue criterion. Tori of this winding number…

We present examples which show that in dimension higher than one or codimension higher than two, there exist toric ideals I_A such that no binomial ideal contained in I_A and of the same dimension is a complete intersection. This result has…

It is a well-known result that, in projective space over a field, every set-theoretical complete intersection of positive dimension in connected in codimension one (Hartshorne [H1,3.4.6] or [H2, Theorem 1.3]). Another important…

Newstead and Ramanan conjectured the vanishing of the top (2g-1) Chern classes of the moduli space of stable, odd degree vector bundles of rank 2 on a Riemann surface of genus g. This was proved by Gieseker [G], while an analogue in rank 3…

We investigate the possible disappearance of Mott oscillations in the scattering of bosonic nuclei at sub-barrier energies. This effect is universal and happens at a critical value of the Sommerfeld parameter. It is also found that the…