We compute (algebraically) the Euler characteristic of a complex of sheaves with constructible cohomology. A stratified Poincaré-Hopf formula is then a consequence of the smooth Poincaré-Hopf theorem and of additivity of the Euler-Poincaré characteristic with compact supports, once we have a suitable definition of index. AMS classification: 55N33 57R25

In this paper, we investigate some properties of inverse limits of linear algebraic groups. For example, we show that if G = lim ←−Gi, where (Gi, πji)i,j∈I is an inverse system of algebraic groups over an algebraically closed field. Then each canonical projection πi : G → Gi maps closed subgroups of G onto closed subgroups of Gi. Furthermore, we prove directly that the inverse limit of an inver...

Let X be a rational nonsingular compact connected real algebraic surface. Denote by Diffalg(X) the group of algebraic diffeomorphisms of X into itself. The group Diffalg(X) acts diagonally on X n, for any natural integer n. We show that this action is transitive, for all n. As an application we give a new and simpler proof of the fact that two rational nonsingular compact connected real algebra...

Let T * C* x C* act meromorphically on a compact Kahler manifold X, e.g. algebraically on a projective manifold. The following is a basic question from geometric invariant theory whose answer is unknown even if .Vis projective. PROBLEM. Classify all T-invariant open subsets U of X such that the geometricquotient U —> U/Texists with U/Ta compact complex space (necessarily algebraic if Xis). In t...

Abstract Let $p$ be a prime number and $k$ an algebraically closed field with characteristic $\ell \neq p$. We show that the supercuspidal support of irreducible smooth $k$-representations Levi subgroups $\textrm {M}^{\prime}$ {SL}_n(F)$ is unique up to {M}^{\prime}$-conjugation, where $F$ either finite or non-Archimedean locally compact residual $p$.

Let G be a group and let V an algebraic over algebraically closed field. We introduce subshifts ? ? VG which generalize both the class of sofic finite alphabets. When is polycyclic-by-finite group, we show that satisfies descending chain condition notion subshifts, type are all equivalent. Thus, obtain extensions well-known results Kitchens Schmidt to cover case many non-compact

Specification and maintenance of relationships between models are vital for MDE. We show that a wide class of such relationships can be specified in a compact and precise manner if intermodel mappings involve derived model elements computed by corresponding queries. Composition of such mappings is not straightforward and requires specialized algebraic machinery. We present a formal framework, i...

‎let $l$ be a lie algebra‎, ‎$mathrm{der}(l)$ be the set of all derivations of $l$ and $mathrm{der}_c(l)$ denote the set of all derivations $alphainmathrm{der}(l)$ for which $alpha(x)in [x,l]:={[x,y]vert yin l}$ for all $xin l$‎. ‎we obtain an upper bound for dimension of $mathrm{der}_c(l)$ of the finite dimensional nilpotent lie algebra $l$ over algebraically closed fields‎. ‎also‎, ‎we classi...

The base space of an algebraically completely integrable Hamiltonian system acquires a rather special differential-geometric structure which plays an important role in modern physical theories such as Seiberg-Witten theory. This structure was formalised by D. Freed [1] as a Special Kähler manifold. In that paper he conjectured that there are no compact special Kähler manifolds other than flat o...