Related papers: Cherlin's conjecture for sporadic simple groups

We show that a generically sharply $t$-transitive permutation group of finite Morley rank on a set of rank $r$ satisfies $t\le r+2$ provided the pointwise stabilizer of a generic $(t-1)$-tuple is an $L$-group, which holds, for example, when…

In this (partly expository) paper we show, using ideas from the theory of total positivity, how a number of properties of a semisimple group over the complex numbers can be presented purely in terms of the Weyl group. We also describe some…

Using the Luthar--Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the Suzuki sporadic simple group Suz. As a consequence, for this group we confirm the Kimmerle's…

In this paper, we proved that a log smooth family of log general type klt pairs with a special (in the sense of Campana) quasi-projective base is isotrivial. As a consequence, we proved the generalized Kebekus-Kov\'acs conjecture…

In this article we study the K- and L-theory of groups acting on trees. We consider the problem in the context of the fibered isomorphism conjecture of Farrell and Jones. We show that in the class of residually finite groups it is enough to…

The notion of a gerbe with connection is conveniently reformulated in terms of the simplicial deRham complex. In particular the usual Chern-Weil and Chern-Simons theory is well adapted to this framework and rather easily gives rise to…

We prove the Baum-Connes conjecture for hyperbolic groups and their subgroups.

Recently, Moret\'o and Rizo proposed a conjecture, known as the Picky Conjecture, proposing new character correspondences extending the McKay Conjecture. We prove the Picky Conjecture for all quasi-simple groups of Lie type for non-defining…

A conjecture of Beauville and Voisin states that for an irreducible symplectic variety X, any polynomial relation between classes of divisors and the Chern classes of X which holds in cohomology already holds in the Chow groups. We verify…

We classify simple groups that act by birational transformations on compact complex K\"ahler surfaces. Moreover, we show that every finitely generated simple group that acts non-trivially by birational transformations on a projective…

In this note, we propose a conjecture stating that some series involving primitive sequences are convergent. Then, we show (by a counterexample) that the analogue of a conjecture of Erd\H{o}s, for those series, is false.

We determine the group of endotrivial modules (as an abstract group) for $G$ a (quasi)simple group of sporadic type, extending previous results in the literature. In many sporadic cases we directly construct the subgroup of trivial-source…

In this article, we prove a strong relative Novikov conjecture for any pair of groups that are coarsely embeddable into Hilbert space.

We describe sofic groupoids in elementary terms and prove several permanence properties for sofcity. We show that sofcity can be determined in terms of the full group alone, answering a question by Conley, Kechris and Tucker-Drob.

For a central simple algebra with a symplectic involution (A,s) over a field of characteristic different from 2, we show that its group of projective similitudes PSim(A,s) is R-trivial in two new cases.

We show that the sporadic simple group $\M(22)$, the exceptional group of Lie type ${}^2\E_6(2)$ and their automorphism groups are uniquely determined by the approximate structure of the centralizer of an element of order 3 together with…

A.A. Suslin proved a normality theorem for an elementary linear group, which says that an elementary linear group of size bigger than or equal to 3 over a commutative ring with unity is normal in the general linear group of same size.…

We show how the existing proof of the Farrell-Jones Conjecture for virtually poly-$\mathbb{Z}$-groups can be improved to rely only on the usual inheritance properties in combination with transfer reducibility as a sufficient criterion for…

We prove equivariant versions of the Beilinson-Lichtenbaum conjecture for Bredon motivic cohomology of smooth complex and real varieties with an action of the group of order two. This identifies equivariant motivic and topological…

Motivated by the generalized Bloch conjecture, we formulate a conjecture about the Chow groups of Pl\"ucker hypersurfaces in Grassmannians. We prove weak versions of this conjecture.