Commutative Algebra Papers of the Week

We construct an explicit minimal cellular resolution for every squarefree monomial ideal generated in degree $n-2$ in the polynomial ring $S=K[x_1,\ldots,x_n]$.

We prove that $\mathbf D^+_{\mathrm{fg},W}(R)=\operatorname{Loc}_{\mathrm{ex}}(\mathbf D^b_{\mathrm{fg},W}(R))$ whenever $W\subseteq\operatorname{Spec} R$ is specialization closed and has finite dimension.

Let $M$ be a finitely generated module over a ring $R$ that is a finitely generated algebra over a Noetherian ring $A$ by $r$ elements. We prove that there are finitely many primes $P_1, \ldots, P_k$ of $A$ such that $M$ has a countable ascending filtration by finitely generated $A$-modules with the property that every factor $F_n$ has a filtration by cyclic modules of the form $A/P_i$, $1 \leq i \leq k$ such that the number of copies $H_i(n)$ of $A/P_i$ that occur in the filtration of $F_n$ is an eventually polynomial function of $n$.

For every ideal of minors of a generic complex matrix, we determine all roots and their multiplicities in the Bernstein-Sato polynomial.

We prove a Reider-type theorem for syzygies: for every integer $p\ge 0$, the adjoint divisor $K_X+\pi^*A$ satisfies Property $\mathrm{N}_p$ provided that $A\cdot C\geq p+3$ for every curve $C\subseteq S$ with $C^2\le 1$.

We determine the maximum number of common zeros in projective space of any set of linearly independent homogeneous polynomials of the same degree, when the degree is smaller than the cardinality of the finite field.

Specifically, we prove that it is coherent if and only if $V$ is almost maximal, and either $\Gamma = \mathbb{R}$ or $\Gamma$ is discrete.

We prove the conjectured formula for arbitrary $m$ when $\binom{m+d}{d}-\binom{d+2}{2}<r\leq\binom{m+d}{d}$.

We describe the obstruction to descent from the AGCD domain $D_S$ by bounded $S$-torsion and by a finiteness condition on intersections of principal ideals.

The goal of this paper is to provide lower and upper bounds on the ordinals that are needed to construct final coalgebras over $R$-modules as the limit of a transfinite sequence of functor iterations.

We study the integer-valued polynomial ring with the stacked-bases property, maximal ideals above valuation ideals, and the polynomial closure of matrices with prescribed characteristic polynomials.

We study the tensor triangular geometry of derived categories of valuation domains, obtaining complete ring-theoretic characterizations of their main structural properties.

In this paper, we investigate the Quillen cohomology of divided power algebras over an operad 𝒫 , identifying Beck modules, derivations, and Kähler differentials in that setup.

We prove that if $I$ is $\mathbf{a}$-bounded and $M$ is a positively $\mathbf{b}$-determined $R$-module, then $\mathrm{tr}_R(M)$ is $(\mathbf{a}+\mathbf{b})$-bounded.

This paper constructs the cohomology theory for grading-restricted vertex superalgebras, generalizing Yi-Zhi Huang's cohomology theory of grading-restricted vertex algebras.

Soc., 1938). In this work, we study isomorphism testing of tensors over commutative rings from a complexity-theoretic viewpoint, and its applications.

We introduce nearly determinantal matrices and study their ideals of $2$-minors.

We give a complete classification of all Koszul licci ideals, including a complete description of the defining equations and graded Betti tables for these ideals, showing that they exactly correspond to quadratic licci ideals that are at most two links away from a complete intersection.