Related papers: Dieudonn\'e theory over semiperfect rings and perf…
The structure of the reduction of an admissible $G$-covering $Y \to X$ at primes $p$ dividing $|G|$ is investigated. Assume $|G|$ is not divisible by $p^2$ and the $p$-Sylow group is normal. Following Raynaud it is shown that there is a…
In this paper, we extend the classical theory of crossed $G$-sets and the crossed Burnside ring from a finite group $G$ to a finite groupoid $\mathcal{G}$. We introduce a natural monoidal structure on the category of crossed…
For a smooth projective scheme $X$ over a ring $R$ on which $p$ is nilpotent that meets some general assumptions we prove that the crystalline cohomology is equipped with the structure of a higher display which is a relative version of…
An approach to identify the normal subgroups determined by ideals in free group rings with the help of the derived functors of non-additive functors is explored. A similar approach, i.e., via derived functors, for computing limits of…
We ascertain conditions and structures on categories and semigroups which admit the construction of pseudo-products and trace products respectively, making their connection as precise as possible. This topic is modelled on the ESN Theorem…
Consider a pseudo-$H$-space $E$ endowed with a separately continuous biadditive associative multiplication which induces a grading on $E$ with respect to an abelian group $G$. We call such a space a graded pseudo-$H$-ring and we show that…
We classify thick subcategories of the $\infty$-categories of perfect modules over ring spectra which arise as functions on even periodic derived stacks satisfying affineness and regularity conditions. For example, we show that the thick…
We study the Duflot filtration on the Borel equivariant cohomology of smooth manifolds with a smooth $p$-torus action. We axiomatize the filtration and prove analog of several structural results about equivariant cohomology rings in this…
A Liouville-type result for the p-Laplacian on complete Riemannian manifolds is proved. As an application are present some results concerning complete non-compact hypersurfaces immersed in a suitable warped product manifold.
We study products of the affine geometric crystal of type A corresponding to symmetric powers of the standard representation. The quotient of this product by the R-matrix action is constructed inside the unipotent loop group. This quotient…
We develop the theory of group graded division ring parallel to the one by P. Cohn for (ungraded) division rings.
The lattice of fully invariant subgroups of an abelian $p$--group and the lattice of ideals of its endomorphism ring are classified by systems of cardinal invariants.
We characterize those finite groups for which the bounded derived category of finite dimensional representations over an algebraically closed field of characteristic $p$ has distributive lattice of thick subcategories: they are precisely…
We give necessary and sufficient conditions on the graph of a right-angled Artin group that determine whether the group is subgroup separable or not. Moreover, we investigate the profinite topology of the direct product of two free groups.…
We introduce the notion of a prism, which may be regarded as a "deperfection" of the notion of a perfectoid ring. Using prisms, we attach a ringed site -- the prismatic site -- to a $p$-adic formal scheme. The resulting cohomology theory…
The global dimension of a ring governs many useful abilities. For example, it is semi-simple if the global dimension is 0, hereditary if it is 1 and so on. We will calculate the global dimension of a Crystalline Graded Ring, as defined in…
Various algebraic structures in geometry and group theory have appeared to be governed by certain universal rings. Examples include: the cohomology rings of Hilbert schemes of points on projective surfaces and quasi-projective surfaces; the…
Building on recent work of Jaikin-Zapirain, we provide a homological criterion for a ring to be a pseudo-Sylvester domain, that is, to admit a division ring of fractions over which all stably full matrices become invertible. We use the…
The structure of transformation semigroups on a finite set is analyzed by introducing a hierarchy of functions mapping subsets to subsets. The resulting hierarchy of semigroups has a corresponding hierarchy of minimal ideals, or kernels.…
We investigate a semigroup construction generalising the two-sided wreath product. We develop the foundations of this construction and show that for groups it is isomorphic to the usual wreath product. We also show that it gives a slightly…