Related papers: New examples of p-adically rigid automorphic forms

We investigate the concept of definable, or inner, automorphism in the logical setting of partial Horn theories. The central technical result extends a syntactical characterization of the group of such automorphisms (called the covariant…

In this paper we study the existence of at least one non-inner automorphism of order p in a finite normally constrained p-group when p is an odd prime.

We classify unital associative conformal algebras of linear growth and provide new examples of such.

The homotopy type and homotopy groups of some spectra TAF of topological automorphic forms associated to a unitary similitude group GU of type (1,1) are explicitly described in quasi-split cases. The spectrum TAF is shown to be closely…

Presentations for the holomorphs of abelian groups of the form $C_{p^n} \times 1^{m}$ for $p$=2 or an odd prime are given. These presentations extend the results given in Burnside's well-known text on finite groups on the holomorphs for the…

Let $\mathcal{L}$ be a centric linking system associated to a saturated fusion system on a finite $p$-group $S$. An automorphism of $\mathcal{L}$ is said to be rigid if it restricts to the identity on the fusion system. An inner rigid…

Nikulin-type orbifolds are certain singular 4-dimensional irreducible holomorphic symplectic varieties. We show that the monodromy group of Nikulin-type orbifolds is maximal and classify finite order symplectic automorphisms up to…

Let A be an abelian variety over C such that the semisimple part of the Hodge group of A is a product of copies of SU(p,1) for some p>1. We show that any effective Tate twist of a Hodge structure occurring in the cohomology of A is…

We outline a new approach to classify real forms and automorphisms of finite order of affine Kac-Moody algebras.

We construct a semi-stable formal model of a wide open rigid curve with a semi-stable covering, and study the l-adic cohomology of the rigid curve. We describe the l-adic cohomology of the rigid curve using the l-adic cohomology of the…

Many common finite p-groups admit automorphisms of order coprime to p, and when p is odd, it is reasonably difficult to find finite p-groups whose automorphism group is a p-group. Yet the goal of this paper is to prove that the automorphism…

We describe the structure of the algebraic group of automorphisms of all simple finite dimensional Lie superalgebras. Using this and \'etale cohomology considerations, we list all different isomorphism classes of the corresponding twisted…

We determine the permutation groups that arise as the automorphism groups of cyclic combinatorial objects. As special cases we classify the automorphism groups of cyclic codes. We also give the permutations by which two cyclic combinatorial…

We improve a result of Prokhorov and Shramov on the rank of finite $p$-subgroups of the birational automorphism group of a rationally connected variety. Known examples show that they are sharp in many cases.

We study some automorphic cohomology classes of degree one on the Griffiths-Schmid varieties attached to some unitary groups in 3 variables. Using partial compactifications of those varieties, constructed by K. Kato and S. Usui, we define…

We determine the structure of automorphism group or each nonsplit metacyclic 2-group. This completes the work on automorphism groups of metacyclic $p$-groups.

We prove rigidity of various types of holomorphic parabolic geometry on smooth complex projective varieties.

We establish direct isomorphisms between different versions of tiling cohomology. The first version is the direct limit of the cohomologies of the approximants in the Anderson-Putnam-G\"ahler complex, the second is the recently introduced…

In this short survey article, we try to list maximum number of known results on class preserving automorphisms of finite $p$-groups. We conclude the survey with some interesting (at least for the author) open problems on this topic.

Let G be a unitary, symplectic or special orthogonal group over a locally compact non-archimedean local field of odd residual characteristic. We construct many new supercuspidal representations of G, and Bushnell-Kutzko types for these…