Related papers: Euler characteristics and compact p-adic Lie group…

Let A be the path algebra of a quiver Q with no oriented cycle. We study geometric properties of the Grassmannians of submodules of a given A-module M. In particular, we obtain some sufficient conditions for smoothness, polynomial…

A locally compact groupoid is said to have the weak containment property if its full $C^*$-algebra coincides with its reduced one. This property is strictly weaker than amenability and is known to be equivalent to amenability for…

Let $X$ be a complex smooth quasi-projective surface acted upon by a finite group $G$ such that the quotient $X/G$ has singularities only of ADE type. We obtain an explicit expression for the generating series of the Euler characteristics…

Let $(A,\mathfrak{m})$ be a Noetherian local ring, $M$ a finite $A$-module and $x_1,...,x_n\in \m$ such that $\lambda (M/\x M)$ is finite. Serre proved that all partial Euler characteristics of $M$ with respect to $\x$ is non-negative. This…

We use the Euler characteristic of the orbit category of a finite group to establish equivalences between theorems of Frobenius and K.S. Brown and between theorems of Steinberg and L. Solomon.

The congruence subgroups $\Gamma_1(m,p)$ that we consider here are subgroups of $GL_m(\Z)$ that fix the vector $(0,\dots,0,1) \mod p$, where $p\geq 5$ is a prime. We present a method and many computations of homological Euler…

The main objective of this project is to determine all irreducible modules of a given modular Lie algebra. In contrast to ordinary Lie algebras, modular Lie algebras require an additional structure known as the p-mapping. The minimal…

For a split reductive algebraic group, this paper observes a homological interpretation for Weyl module multiplicities in Jantzen's sum formula. This interpretation involves an Euler characteristic built from Ext groups between integral…

The set of the first Hilbert coefficients of parameter ideals relative to a module--its Chern coefficients--over a local Noetherian ring codes for considerable information about its structure--noteworthy properties such as that of…

The Euler characteristic can be defined as a special kind of valuation on finite distributive lattices. This work begins with some brief consideration on the role of the Euler characteristic on NM algebras, the algebraic counterpart of…

One of the algebraic structures that has emerged recently in the study of the operator product expansions of chiral fields in conformal field theory is that of a Lie conformal algebra [K]. A Lie pseudoalgebra is a generalization of the…

We study generic properties of topological groups in the sense of Baire category. First we investigate countably infinite (discrete) groups. We extend a classical result of B. H. Neumann, H. Simmons and A. Macintyre on algebraically closed…

We define global and local Weyl modules for Lie superalgebras of the form $\mathfrak{g} \otimes A$, where $A$ is an associative commutative unital $\mathbb{C}$-algebra and $\mathfrak{g}$ is a basic Lie superalgebra or $\mathfrak{sl}(n,n)$,…

We show how to count and randomly generate finitely generated subgroups of the modular group $\textsf{PSL}(2,\mathbb{Z})$ of a given isomorphism type. We also prove that almost malnormality and non-parabolicity are negligible properties for…

We prove a "twist-compatibility" result for p-adic families of cohomology classes associated to symmetric spaces. This shows that a single family of classes (lying in a finitely-generated Iwasawa module) interpolates classical cohomology…

Let G be a countable discrete group and let M be a smooth proper cocompact G-manifold without boundary. The Euler operator defines via Kasparov theory an element, called the equivariant Euler class, in the equivariant K-homology of M. The…

Let $M^{r}$ be a connected orientable manifold with the Euler characteristic $\chi(M)\not \equiv 0\operatorname{mod}6$. Denote by $\mathrm{SAut}(F_{n})$ the unique subgroup of index two in the automorphism group of a free group. Then any…

We show that when $A$ is a reduced algebra over a characteristic zero field $k$ and the module of K\"ahler differentials $\Omega_{A/k}=0$, then $A$ is ind-\'etale, partially answering a question of Bhatt. As further applications of this…

It is well known that, for any finitely generated torsion module M over the Iwasawa algebra Z_p [[{\Gamma} ]], where {\Gamma} is isomorphic to Z_p, there exists a continuous p-adic character {\rho} of {\Gamma} such that, for every open…

We study the cohomology of an elliptic differential complex arising from the infinitesimal moduli of heterotic string theory. We compute these cohomology groups at the standard embedding, and show that they decompose into a direct sum of…