Related papers: Rigid local systems and alternating groups

We study the problem of realizing families of subgroups as the set of stabilizers of configurations from a subshift of finite type (SFT). This problem generalizes both the existence of strongly and weakly aperiodic SFTs. We show that a…

We study the general properties of certain rank four rigid local systems considered by Goursat. We analyze when they are irreducible, give an explicit integral description as well as the invariant Hermitian form when it exists. By a…

A conjecture of Berkovich asserts that every non-simple finite p-group has a non-inner automorphism of order p. This conjecture is far from being proved despite the great effort devoted to it. In this paper we prove it for p-groups of…

We present new computational results for symplectic monodromy groups of hypergeometric differential equations. In particular, we compute the arithmetic closure of each group, sometimes justifying arithmeticity. The results are obtained by…

In this article, we study the properties of profinite geometric iterated monodromy groups associated to polynomials. Such groups can be seen as generic representations of absolute Galois groups of number fields into the automorphism group…

We study the middle convolution of local systems on the punctured affine line in the setting of singular cohomology and in the setting of \'etale cohomology. We derive a formula to compute the topological monodromy of the middle convolution…

We prove that for any prime $p>2$, $q=p^\nu$ a power of $p$, $n\ge p$ and $G=S_n$ or $G=A_n$ (symmetric or alternating group) there exists a Galois extension $K/\mathbb F_q(T)$ ramified only over $\infty$ with $\mathrm{Gal}(K/\mathbb…

In this paper, we study groups of automorphisms of algebraic systems over a set of $p$-adic integers with different sets of arithmetic and coordinate-wise logical operations and congruence relations modulo $p^k,$ $k\ge 1.$ The main result…

Associated to an abelian variety over a number field are several interesting and related groups: the motivic Galois group, the Mumford-Tate group, $\ell$-adic monodromy groups, and the Sato-Tate group. Assuming the Mumford-Tate conjecture,…

Let $G$ be a group and let $k$ be a field. Kaplansky's direct finiteness conjecture states that every one-sided unit of the group ring $k[G]$ must be a two-sided unit. In this paper, we establish a geometric direct finiteness theorem for…

Let $\sigma$ denote an endomorphism of a smooth algebraic group $G$ over the algebraic closure of a finite field, and assume all iterates of $\sigma$ have finitely many fixed points. Steinberg gave a formula for the number of fixed points…

For finite p-groups P of class 2 and exponent p the following are invariants of fully refined central decompositions of P: the number of members in the decomposition, the multiset of orders of the members, and the multiset of orders of…

In this note we develop some properties of those algebras (called here locally simple) which can be generated by a single element after, if need be, a faithfully flat extension. For finite algebras, this is shown to be in fact a property of…

The finite monodromy groups of abelian varieties over number fields have been introduced by Grothendieck. They represent the local obstruction to semi-stable reduction. In this paper we prove a criteria for finite groups to be realized as…

Many of the conjectures of current interest in the representation theory of finite groups in characteristic $p$ are local-to-global statements, in that they predict consequences for the representations of a finite group $G$ given data about…

Let X be a normal complex algebraic variety, and p a prime. We show that there exists an integer N=N(X, p) such that: any non-trivial, irreducible representation of the fundamental group of X, which arises from geometry, must be non-trivial…

We discuss the finiteness of the topological entropy of continuous endomorphims for some classes of locally compact groups. Firstly, we focus on the abelian case, imposing the condition of being compactly generated, and note an interesting…

The additivity with respect to exact sequences is notoriously a fundamental property of the algebraic entropy of group endomorphisms. It was proved for abelian groups by deeply exploiting their structure. On the other hand, a solvable…

Let $M$ be a locally symmetric irreducible closed manifold of dimension $\ge 3$. A result of Borel [Bo] combined with Mostow rigidity imply that there exists a finite group $G = G(M)$ such that any finite subgroup of $\text{Homeo}^+(M)$ is…

We consider an amalgam of groups constructed from fusion systems for different odd primes p and q. This amalgam contains a self-normalizing cyclic subgroup of order pq and isolated elements of order p and q.