Related papers: B-pairs and (phi,Gamma)-modules

The category of all $k$-algebras with a bilinear form, whose objects are all pairs $(R,b)$ where $R$ is a $k$-algebra and $b\colon R\times R\to k$ is a bilinear mapping, is equivalent to the category of unital $k$-algebras $A$ for which the…

Based on our previous work on an arithmetic analogue of Christol's theorem, this paper studies in more detail the structure of the lambda-ring $E_K = K \otimes W_{O_K}^a (O_{\bar{K}})$ of algebraic Witt vectors for number fields $K$. First…

We construct a monoidal category $\mathscr{C}_{w,v}$ which categorifies the doubly-invariant algebra $^{N'(w)}\mathbb{C}[N]^{N(v)}$ associated with Weyl group elements $w$ and $v$. It gives, after a localization, the coordinate algebra…

We prove a classification result for a large class of noncommutative Bernoulli crossed products $(P,\phi)^\Lambda \rtimes \Lambda$ without almost periodic states. Our results improve the classification results from [1], where only Bernoulli…

The main result is Theorem: Let A be an R-algebra, mu, lambda be cardinals such that |A|<=mu=mu^{aleph_0}<lambda<=2^mu. If A is aleph_0-cotorsion-free or A is countably free, respectively, then there exists an aleph_0-cotorsion-free or a…

Let A be a regular domain of dimension d containing an infinite field and let n be an integer with 2n\geq d+3. For a stably free A-module P of rank n, we prove that (i) P has a unimodular element if and only if the euler class of P is zero…

We give a classification of rank one $(\varphi,\Gamma)$-modules with coefficients in a $p$-adically complete $\mathbf{Z}_p$-algebra. As a consequence, we obtain a new proof of Proposition 7.2.17 in {arXiv:1908.07185}, which gives an…

Let V be a p-adic representation of the absolute Galois group G of Q_p that becomes crystalline over a finite tame extension, and assume p odd. We provide necessary and sufficient conditions for V to be isomorphic to the Tate module V_p(A)…

We study polynomial functors of degree 2, called quadratic, with values in the category of abelian groups $Ab$, and whose source category is an arbitrary category $\C$ with null object such that all objects are colimits of copies of a…

In this article we analyze the structure of $2$-categories of symmetric projective bimodules over a finite dimensional algebra with respect to the action of a finite abelian group. We determine under which condition the resulting…

For any complex parameters a,b, the W(a,b) algebra is the Lie algebra with basis {L_i,W_i|i\in Z}, and relations [L_i,L_j]=(j-i)L_{i+j}, [L_i,W_j]=(a+j+bi)W_{i+j},[W_i,W_j]=0. In this paper, indecomposable modules of the intermediate series…

In the work we have considered Breuil-Kisin module over the ring of witt vectors $W(\kappa)$ over the residue field $\kappa$ of characteristic $p$ and a finite flat $\mathbb{Z}_p$-algebra $R$. Then considered Breuil-Kisin modules $M$ over…

We study the category of modules admitting compatible actions of the Lie algebra $\mathcal{V}$ of vector fields on an affine space and the algebra $\mathcal{A}$ of polynomial functions. We show that modules in this category which are…

Let $R$ be a commutative Noetherian ring and let $\G$ be the category of modules of G-dimension zero over $R$. We denote the associated stable category by $\pG$. We show that the functor category $\modpG$ is a Frobenius category and we…

Let O\_K be a complete discrete valuation ring. Denote by K its fractions field and by k its residue field. Assume that k is of characteristic p>0 and perfect. Breuil gives an anti-equivalence between the category of finite flat O\_K-group…

The category $\mathrm{FI}_G$ was first defined and explored by Sam-Snowden. Here, we develop more of the machinery of $\mathrm{FI}_G$-modules and find numerous examples to apply it to, extending the work of Church-Ellenberg-Farb and Wilson.…

We prove a Tannaka duality theorem for $(\infty,1)$-categories. This is a duality between certain derived group stacks, or more generally certain derived gerbes, and symmetric monoidal $(\infty,1)$-categories endowed with particular…

We give an explicit (new) morphism of modules between $H^*_T(G/P) \otimes H^*_T(P/B)$ and $H^*_T(G/B)$ and prove (the known result) that the two modules are isomorphic. Our map identifies submodules of the cohomology of the flag variety…

We establish the feasibility of investigating the theory of $R\text{-}\mathrm{Mod}$-enriched categories, for any commutative and unitary ring $R$, through the framework of $\mathbb{A}\mathrm{b}$-enriched category theory. In particular, we…

A pair of adjoint functors $(F,G)$ is called a Frobenius pair of the second type if $G$ is a left adjoint of $\beta F\alpha$ for some category equivalences $\alpha$ and $\beta$. Frobenius ring extensions of the second kind provide examples…