Related papers: Methods in complete intersections in corank one

We study the vanishing of (co)homology along ring homomorphisms for modules that admit certain filtrations, and generalize a theorem of O. Celikbas-Takahashi. Our work produces new classes of rigid and test modules, in particular over local…

We give a new approach to intersection theory. Our "cycles" are closed manifolds mapping into compact manifolds and our "intersections" are elements of a homotopy group of a certain Thom space. The results are then applied in various…

A general method for establishing results over a commutative complete intersection local ring by passing to differential graded modules over a graded exterior algebra is described. It is used to deduce, in a uniform way, results on the…

A differential algebra of finite type over a field k is a filtered algebra A, such that the associated graded algebra is finite over its center, and the center is a finitely generated k-algebra. The prototypical example is the algebra of…

A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class--a…

Extending the work of Bell, Matsuzawa and Satriano, we consider a finite set of polynomials $S$ over a number field $K$ and give a necessary and sufficient condition for the existence of a $N \in \mathbb{N}_{> 0}$ and a finite set $Z…

We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…

We introduce the tools of intersection theory to the study of Feynman integrals, which allows for a new way of projecting integrals onto a basis. In order to illustrate this technique, we consider the Baikov representation of maximal cuts…

This paper studies algebraic residual intersections in rings with Serre's condition \( S_{s} \). It demonstrates that residual intersections admit free approaches i.e. perfect subideal with the same radical. This fact leads to determining a…

The general theme of this note is illustrated by the following theorem: Theorem 1. Suppose $K$ is a compact set in the complex plane and 0 belongs to the boundary $\partial K$. Let ${\cal A}(K)$ denote the space of all functions $f$ on $K$…

A direct sum decomposition theory is developed for direct summands (and complements) of modules over a semiring $R$, having the property that $v+w = 0$ implies $v = 0$ and $w = 0$. Although this never occurs when $R$ is a ring, it always…

Let $k$ be a nonperfect separably closed field. Let $G$ be a (possibly non-connected) reductive group defined over $k$. We study rationality problems for Serre's notion of complete reducibility of subgroups of $G$. In our previous work, we…

For every even number $n$, and every $n$-dimensional smooth hypersurface of $\mathbb{P}^{n+1}$ of degree $d$, we compute the periods of all its $\frac{n}{2}$-dimensional complete intersection algebraic cycles. Furthermore, we determine the…

We prove the following results for a unital simple direct limit $A$ of recursive subhomogeneous algebras with no dimension growth: (1) A has stable rank 1. (2) The projections in $M_{\infty} (A)$ satisfy cancellation: if $e \oplus q \sim f…

We describe some connections between three different fields: combinatorics (umbral calculus), functional analysis (linear functionals and operators) and harmonic analysis (convolutions on group-like structures). Systematic usage of…

We take our first step toward getting finite results from the alpha'-corrected D=4 N=4 SYM theory with emphasis on the field theory techniques. Starting with the classical action of N=4 SYM with the leading alpha'-corrections, we examine…

In the note we construct a family of \'etale coverings of the affine line. More specifically, let $F$ be a finite field of characteristic $p$ and suppose that the cardinality of $F$ is at least 4. Let $A = F[T]$ be the polynomial ring in…

Let R be a commutative ring, M an R-module, and N a finitely presented R-module such that the intersection of Max(R) and Supp(N) is finite-dimensional and Noetherian. Suppose also that N is homothetic; in other words, suppose that the…

This article establishes, for an appropriate localisation of associative rings, a long exact sequence in algebraic K-theory. The main result goes as follows. Let A be an associative ring and let A-->B be the localisation with respect to a…

Let K be a comonad on a model category M. We provide conditions under which the associated category of K-coalgebras admits a model category structure such that the forgetful functor to M creates both cofibrations and weak equivalences. We…