Related papers: Frobenius powers of non-complete intersections

If M is a Drinfeld module over a local function field L, we may view M as a dynamical system, and consider its filled Julia set J. If J^0 is the connected component of the identity, relative to the Berkovich topology, we give a…

Let $R$ be a commutative Noetherian local ring. Assume that $R$ has a pair $\{x,y\}$ of exact zerodivisors such that $\dim R/(x,y)\ge2$ and all totally reflexive $R/(x)$-modules are free. We show that the first and second Brauer--Thrall…

It is proved that the sum of the Loewy lengths of the homology modules of a finite free complex F over a local ring R is bounded below by a number depending only on R. This result uncovers, in the structure of modules of finite projective…

Let R be a commutative ring, and let S be a multiplicative subset of R. In this paper, we introduce and investigate the notion of S-FP-injective modules. Among other results, we show that, under certain conditions, a ring R is S-Noetherian…

Let E be an elementary abelian p-group of rank r and let k be a field of characteristic p. We introduce functors F_i from finitely generated kE-modules of constant Jordan type to vector bundles over projective space of dimension r-1. The…

We show, using the techniques developed in arXiv:2504.06444 and arXiv:2305.11139, that dagger algebras and Tate algebras in the sense of Berkovich in prime characteristic $p > 0$ have intersection flat Frobenius. Equivalently, if $S$ is…

There is a well known link from the first topic in the title to the third one. In this paper we thread that link through the second topic. The central result is a criterion for the tensor nilpotence of morphisms of perfect complexes over…

For any polynomial $p\left(x\right)$ over $\mathbb{F}_{l}$ we determine the asymptotic density of hyperelliptic curves over $\mathbb{F}_{q}$ of genus $g$ for which $p\left(x\right)$ divides the characteristic polynomial of Frobenius acting…

The dependence of torsion functors on their supporting ideals is investigated, especially in the case of monomial ideals of certain subrings of polynomial algebras over not necessarily Noetherian rings. As an application it is shown how…

Let $R$ and $S$ be rings and $_R\omega_S$ a semidualizing bimodule. We study when the double functor $\Tor^S_i(\omega, \Ext^i_{R}(\omega,-))$ preserves epimorphisms and the double functor $\Ext_{R}^i(\omega, \Tor_i^{S}(\omega,-))$ preserves…

We prove rigidity type results on the vanishing of stable (co)homology for modules of finite complete intersection dimension, results which generalize and improve upon known results. We also introduce a notion of pre-rigidity, which…

Let $R$ be commutative Noetherian ring and let $\fa$ be an ideal of $R$. For complexes $X$ and $Y$ of $R$--modules we investigate the invariant $\inf{\mathbf R}\Gamma_{\fa}({\mathbf R}\Hom_R(X,Y))$ in certain cases. It is shown that, for…

We introduce the notion of tight homomorphism into a locally compact group with nonvanishing bounded cohomology and study these homomorphisms in detail when the target is a Lie group of Hermitian type. Tight homomorphisms between Lie groups…

An antiferromagnet is a promising material for spin-orbit torque generation. Earlier studies of the spin-orbit torque in an antiferromagnet are limited to collinear spin configurations. We calculate the spin-orbit torque in an…

We study the notions of $n$-hereditary rings and its connection to the classes of finitely $n$-presented modules, FP$_n$-injective modules, FP$_n$-flat modules and $n$-coherent rings. We give characterizations of $n$-hereditary rings in…

Let $S=K[x_1,...,x_n]$ or $S=K[[x_1,...,x_n]]$ be either a polynomial or a formal power series ring in a finite number of variables over a field $K$ of characteristic $p > 0$ with $[K:K^p] < \infty$. Let $R$ be the hypersurface $S/fS$ where…

A nef-partition for a weighted complete intersection is a combinatorial structure on its weights and degrees which is important for Mirror Symmetry. It is known that nef-partitions exist for smooth well-formed Fano weighted complete…

In this note we introduce and study basic properties of two types of modules over a commutative noetherian ring $R$ of positive prime characteristic. The first is the category of modules of finite $F$-type. These objects include reflexive…

It is proved that if $\varphi\colon A\to B$ is a local homomorphism of commutative noetherian local rings, a nonzero finitely generated $B$-module $N$ whose flat dimension over $A$ is at most $\mathrm{edim}\, A - \mathrm{edim}\, B$, is free…

We show that the (topological) full group of a minimal pseudogroup over the Cantor set satisfies various rigidity phenomena of topological dynamical and combinatorial nature. Our main result applies to its possible homomorphisms into other…