Related papers: Free $(\mathbb{Z}/p)^n$-complexes and $p$-DG modul…

In answer to a question of A. Blass, J. Irwin and G. Schlitt, a subgroup G of the additive group Z^{\omega} is constructed whose dual, Hom(G,Z), is free abelian of rank 2^{\aleph_0}. The question of whether Z^{\omega} has subgroups whose…

We investigate homological properties of perfect algebras of prime characteristic. The principle is as follows: perfect algebras resolve the singularities. For example, we show any module over the ring of absolute integral closure has…

We study the commensurators of free groups and free pro-$p$ groups, as well as certain subgroups of these. We prove that the commensurator $Comm(F)$ of a non-abelian free group of finite rank $F$ is not virtually simple, answering a…

We study differential graded algebras whose homology is an exterior algebra over a commutative ring R on a generator of degree n, and also certain types of differential modules over these DGAs. We obtain a complete classification when R is…

We study graduated orders over completed group rings of $1$-dimensional admissible $p$-adic Lie groups, and verify the equivariant $p$-adic Artin conjecture for such orders. Following Jacobinski and Plesken, we obtain a formula for the…

Let G be a connected and reductive algebraic group over an algebraically closed field of characteristic p > 0. An interesting class of representations of G consists of those G-modules having a good filtration -- i.e. a filtration whose…

In this paper, we study the classes of rings in which every proper (regular) ideal can be factored as an invertible ideal times a nonempty product of proper radical ideals. More precisely, we investigate the stability of these properties…

For an odd prime number $p$, we consider degree $p$ extensions $L/K$ of $p$-adic fields with normal closure $\widetilde{L}$ such that the Galois group of $\widetilde{L}/K$ is the dihedral group of order $2p$. We shall prove a complete…

Let $G$ be a simple complex factorizable Poisson Lie algebraic group. Let $\U_\hbar(\g)$ be the corresponding quantum group. We study $\U_\hbar(\g)$-equivariant quantization $\C_\hbar[G]$ of the affine coordinate ring $\C[G]$ along the…

Let p be a prime and G be a torsion-free abelian group. A homomorphism from G to the p-adic integers is called a p-adic functional on G. If G has finite rank, then G can be represented as an inductive limit of an inductive sequence of free…

We introduce a method for associating a chain complex to a module over a combinatorial category, such that if the complex is exact then the module has a rational Hilbert series. We prove homology--vanishing theorems for these complexes for…

If G is a pro-p, p-adic, Lie group and if $\Lambda(G)$ denotes the Iwasawa algebra of G then we present a formula for determining the $\Lambda(G)$-rank of a finitely generated $\Lambda(G)$-module. This is given in terms of the G homology…

We complete the results of a previous article. Let $G$ be a split connected reductive group over a finite extension $F$ of $\mathbb{Q}_p$. When $F=\mathbb{Q}_p$, we determine the extensions between unitary continuous $p$-adic and smooth mod…

We consider recollements of derived categories of dg-algebras induced by self orthogonal compact objects obtaining a generalization of Rickard's Theorem. Specializing to the case of partial tilting modules over a ring, we extend the results…

This paper focuses on the rank varieties for modules over a group algebra $\mathbb{F}E$ where $E$ is an elementary abelian $p$-group and $p$ is the characteristic of an algebraically closed field $\mathbb{F}$. In the first part, we give a…

We prove that for any finite-dimensional differential graded algebra with separable semisimple part the category of perfect modules is equivalent to a full subcategory of the category of perfect complexes on a smooth projective scheme with…

Let G be a connected reductive quasisplit algebraic group over a field L which is a finite extension of the p-adic numbers. We construct an exact sequence modelled on (the dual of) the BGG resolution involving locally analytic principal…

Let p>2 be a rational prime, k be a perfect field of characteristic p and K be a finite totally ramified extension of the fractional field of the Witt ring of k. Let G and H be finite flat commutative group schemes killed by p over O_K and…

In this paper we extend two results of Happel to commutative rings. Let $(A, \mathfrak{m})$ be a commutative Noetherian local ring. Let $D^b_f(mod \ A)$ be the bounded derived category of complexes of finitely generated modules over $A$…

For a commutative ring $R$, we exploit localization techniques and point-free topology to give an explicit realization of both the Zariski frame of $R$ (the frame of radical ideals in $R$) and its Hochster dual frame, as lattices in the…