Let S be an unramified regular local ring of mixed characteristic p≥3 and Sp the subring obtained by lifting to image Frobenius map on S/pS. R integral closure in a biradical extension degree p2 its quotient field adjoining p-th roots sufficiently general square free elements f,g∈Sp. We show that admits birational maximal Cohen-Macaulay module. It is noted not automatically Cohen-Macaulay.

We introduce and study vertex cover algebras of weighted simplicial complexes. These algebras are special classes of symbolic Rees algebras. We show that symbolic Rees algebras of monomial ideals are finitely generated and that such an algebra is normal and Cohen-Macaulay if the monomial ideal is squarefree. For a simple graph, the vertex cover algebra is generated by elements of degree 2, and ...

If V is a faithful module for a nite group G over a eld of characteristic p > 0, then the ring of invariants need not be Cohen-Macaulay if p divides the order of G. In this article the cohomology of G is used to study the question of Cohen-Macaulayness of the invariant ring. Let R = S(V) be the polynomial ring on which G acts. Then the main result can be stated as follow: If H r (G; R) 6 = 0 fo...

We study the singularities of integral models Shimura varieties and moduli stacks shtukas with parahoric level structure. More generally, our results apply to Pappas–Zhu Levin mixed characteristic local models, their equal analogues. For any such model we prove under minimal assumptions that entire is normal reduced special fiber and, if $p > 2$, it also Cohen–Macaulay. This proves a conjecture...

The absolute order on the hyperoctahedral group Bn is investigated. Using a poset fiber theorem, it is proved that the order ideal of this poset generated by the Coxeter elements is homotopy Cohen–Macaulay. This method results in a new proof of Cohen–Macaulayness of the absolute order on the symmetric group. Moreover, it is shown that every closed interval in the absolute order on Bn is shellab...

We prove that the generic quantized coordinate ringOq(G) is Auslander-regular, Cohen-Macaulay, and catenary for every connected semisimple Lie group G. This answers questions raised by Brown, Lenagan, and the first author. We also prove that under certain hypotheses concerning the existence of normal elements, a noetherian Hopf algebra is Auslander-Gorenstein and Cohen-Macaulay. This provides a...

The algebra of basic covers of a graph G, denoted by Ā(G), was introduced by Herzog as a suitable quotient of the vertex cover algebra. In this paper we compute the Krull dimension of Ā(G) in terms of the combinatorics of G. As a consequence, we get new upper bounds on the arithmetical rank of monomial ideals of pure codimension 2. Furthermore, we show that if the graph is bipartite, then Ā(G) ...

We describe some recent work concerning Gorenstein liaison of codimension two subschemes of a projective variety. Applications make use of the algebraic theory of maximal Cohen–Macaulay modules, which we review in an Appendix.

Pinched Veronese rings are formed by removing an algebra generator from a subring of polynomial ring. We study the homological properties such rings, including Cohen-Macaulay, Gorenstein, and complete intersection properties. Greco Martino classified Cohen-Macaulayness pinched maximum entry exponent vector monomial; we re-prove their results with semigroup methods correct omission small class e...

This paper considers the following conjecture: If R is an unmixed, equidimensional local ring that is a homomorphic image of a Cohen-Macaulay local ring, then for any ideal J generated by a system of parameters, the Chern coefficient e1(J) < 0 is equivalent to R being non Cohen-Macaulay. The conjecture is established if R is a homomorphic image of a Gorenstein ring, and for all universally cate...