Related papers: Modular Products and Modules for Finite Groups
We study the construction of tensor products of representations up to homotopy, which are the A-infinity version of ordinary representations. We provide formulas for the construction of tensor products of representations up to homotopy and…
We introduce and study the category of modular (i.e. with coefficient of positive characteristic) monodromic perverse sheaves on complex stratified $T$-varieties, with $T$ a complex algebraic torus. In particular, we show that under…
We study monoids equipped with a second binary operation that captures the structure of the endomorphisms of an object $X$ such that $X=X\times X$. We construct a universal monoid of this type and examine some of its rich combinatorial…
The purpose of this paper is to introduce and study a Hom-type generalization of rings. We provide their basic properties and and some key constructions. Furthermore, we consider modules over Hom-rings and characterize the category of…
We fix an excellent regular noetherian scheme $S$ over ${\mathbf Z}_{(p)}$ satisfying a certain finiteness condition. For a constructible \'etale sheaf ${\cal F}$ on a regular scheme $X$ of finite type over $S$, we introduce a variant of…
We determine the composition factors of the tensor product $S(E)\otimes S(E)$ of two copies of the symmetric algebra of the natural module $E$ of a general linear group over an algebraically closed field of positive characteristic. Our main…
We generalize the results of [KMST] concerning equivariant quantization by means of Verma modules $M(\lambda)$ for generic weight $\lambda$ to the case of general $\lambda$. We consider the relationship between the Shapovalov form on an…
Dave Benson conjectured in 2020 that if $G$ is a finite $2$-group and $V$ is an odd-dimensional indecomposable representation of $G$ over an algebraically closed field $\Bbbk$ of characteristic $2$, then the only odd-dimensional…
We modify the well-known tensor product of modules over a semiring, in order to treat modules over hyperrings, and, more generally, for bimodules (and bimagmas) over monoids. The tensor product of residue hypermodules is functorial. Special…
We exposit the construction of Rademacher sums in arbitrary weights and describe their relationship to mock modular forms. We introduce the notion of Rademacher series and describe several applications, including the determination of…
We derive finite rational formulas for the traces of cycle integrals of certain meromorphic modular forms. Moreover, we prove the modularity of a completion of the generating function of such traces. The theoretical framework for these…
We describe a natural structure of an abelian intertwining algebra (in the sense of Dong and Lepowsky) on the direct sum of the untwisted vertex operator algebra constructed {}from the Leech lattice and its (unique) irreducible twisted…
The Moonshine module is a $c=24$ conformal field theory (CFT) whose automorphism group is the Monster group. It was argued by Dixon, Ginsparg, and Harvey in \cite{Dixon:1988qd} that there exists a spin lift of the Moonshine CFT with…
Recently the author has introduced cobordism-like modules induced from generic maps whose codimensions are negative. They are generalizations of cobordism modules of manifolds. They have been introduced in generalizing the following theorem…
The modular forms are revisited from a geometric and an algebraic point of view leading to a geometric interpretation of the weak Maass forms connecting them to the Ramanujan Mock Theta functions and to the cusp forms generated from the…
A module over a ring $R$ is pure projective provided it is isomorphic to a direct summand of a direct sum of finitely presented modules. We develop tools for the classification of pure projective modules over commutative noetherian rings.…
Our main goal in this paper is to answer new positive cases of the natural generalized version of Hartshorne's celebrated question on cofiniteness of local cohomology modules, and consequently of Huneke's conjecture on the finiteness of…
Let $(R,\fm)$ be a commutative Noetherian local ring. Suppose that $M$ and $N$ are finitely generated modules over $R$ such that $M$ has finite projective dimension and such that $\Tor^R_i(M,N)=0$ for all $i>0$. The main result of this note…
Utilizing a classification due to Lemke Oliver of eta-quotients which are also theta functions (here called eta-theta functions), Folsom, Garthwaite, Kang, Treneer, and the fourth author constructed a catalog of mock modular forms $V_{mn}$…
We generalize the lexicographic product of first-order structures by presenting a framework for constructions which, in a sense, mimic iterating the lexicographic product infinitely and not necessarily countably many times. We then define…