In this paper we show that if q is a power of a prime p , then the projective special linear group PSL(2, q) and the stabilizer of a point of the projective line have maximum sum element orders among all proper subgroups of projective general linear group PGL(2, q) for q odd and even respectively

Using the localization property, we construct triangulated categories of motives over quasi-projective $T$-schemes for any coefficient where $T$ is a noetherian separated scheme, and prove Grothendieck six operations formalism. We also integral étale realization motives.

Consider a diagram of quasi-categories that admit and functors that preserve limits or colimits of a fixed shape. We show that any weighted limit whose weight is a projective cofibrant simplicial functor is again a quasi-category admitting these (co)limits and that they are preserved by the functors in the limit cone. In particular, the BousfieldKan homotopy limit of a diagram of quasi-categori...

We prove two results relating 3-manifold groups to fundamental groups occurring in complex geometry. Let N be a compact, connected, orientable 3-manifold. If N has non-empty, toroidal boundary, and π1(N) is a Kähler group, then N is the product of a torus with an interval. On the other hand, if N has either empty or toroidal boundary, and π1(N) is a quasi-projective group, then all the prime co...

We will introduce the notion of Gorenstein category as the convenient setup for doing Gorenstein Homological Algebra in categories of sheaves, or in general in categories without enough projective objects. We will illustrate this notion by showing that the category of Qcoh(X) of quasi-coherent sheaves on a locally Gorenstein projective scheme fits into this setup. Then we will focus on the cate...

in this paper we show that if q is a power of a prime p , then the projective special linear group psl(2, q) and the stabilizer of a point of the projective line have maximum sum element orders among all proper subgroups of projective general linear group pgl(2, q) for q odd and even respectively

The semi-topological K-theory of a complex variety was defined in [FW2] with the expectation that it would prove to be a theory lying “part way” between the algebraic K-theory of the variety and the topological K-theory of the associated analytic space, and thus would share properties with each of these other theories. In this paper, we realize these expectations by proving among other results ...

We construct certain modified highest weight modules which are called quasi in this paper. Using the modules, we introduce a new category of over an affine Lie superalgebra contains projective covers. also prove that both these covers and satisfy vanishing property BRST cohomology.