Related papers: Finiteness for self-dual classes in integral varia…

A flat vector bundle on an algebraic variety supports two natural definable structures given by the flat and algebraic coordinates. In this note we show these two structures coincide, subject to a condition on the local monodromy at…

In the course of classifying the homogeneous permutations, Cameron introduced the viewpoint of permutations as structures in a language of two linear orders, and this structural viewpoint is taken up here. The majority of this thesis is…

We partially resolve conjectures of Deligne and Simpson concerning $\mathbb{Z}$-local systems on quasi-projective varieties that underlie a polarized variation of Hodge structure. For local systems with $\mathbb{Q}$-anisotropic monodromy,…

We introduce and study asymptotically rigid mapping class groups of certain infinite graphs. We determine their finiteness properties and show that these depend on the number of ends of the underlying graph. In a special case where the…

This is the second in a trilogy of papers introducing and studying the notion of decomposition space as a general framework for incidence algebras and M\"obius inversion, with coefficients in $\infty$-groupoids. A decomposition space is a…

A variation of Hodge structure is a horizontal holomorphic mapping into a flag domain D; here "horizontal" indicates that the image of the map satisfies a system of partial differential equations known as the infinitesimal period relation…

We show that the homological finiteness length of a non-uniform lattice on a locally finite CAT(0) n-dimensional polyhedral complex is less than n. As a corollary, we obtain an upper bound for the homological finiteness length of arithmetic…

In this article we study a class of central extensions of $\mathbb{Z}\wr\mathbb{Z}$, as first described by Hall. On the one hand, we consider groups of this type with cyclic centre, our construction yields a rich class of groups. In…

We offer a criterion for showing that the automorphism group of an ultrahomogeneous structure is topologically 2-generated and even has a cyclically dense conjugacy class. We then show how finite topological rank of the automorphism group…

In the recent paper arXiv:1807.02721, B. Lawrence and A. Venkatesh develop a method of proving finiteness theorems in arithmetic geometry by studying the geometry of families over a base variety. Their results include a new proof of both…

Using a categorial version of Fra\"iss\'e's theorem due to Droste and G\"obel, we derive a criterion for a comma-category to have universal homogeneous objects. As a first application we give new existence result for universal structures…

In this note, we aim to prove the finite semi-algebraic chamber decomposition theorem for K-semi(poly)stability under the assumption of the log boundedness of K-semistable degenerations. This boundedness assumption is naturally arising from…

Homomorphism duality pairs play crucial role in the theory of relational structures and in the Constraint Satisfaction Problem. The case where both classes are finite is fully characterized. The case when both side are infinite seems to be…

This is the second of two papers that describe a compactness theorem for sequences of solutions of certain SL(2;C) analogs of the anti-self dual equations on oriented, 4-dimensional Riemannian manifolds. This paper proves theorems that…

In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…

We introduce asymptotically rigid mapping class groups of handlebodies and determine their finiteness properties, which vary depending on the space of ends of the underlying handlebody. As it turns out, in some cases, the homology of these…

We discuss in the context of finite extensions two classical theorems of Takahasi and Howson on subgroups of free groups. We provide bounds for the rank of the intersection of subgroups within classes of groups such as virtually free…

Green and Griffiths have introduced several notions of singularities associated with normal functions, especially in connection with middle dimensional primitive Hodge classes. In this note, by using the more elementary aspects of the…

We define a family of groups that generalises Thompson's groups $T$ and $G$ and also those of Higman, Stein and Brin. For groups in this family we descrine centralisers of finite subgroups and show, that for a given finite subgroup $Q$,…

In despair, as Deligne (2000) put it, of proving the Hodge and Tate conjectures, we can try to find substitutes. For abelian varieties in characteristic zero, Deligne (1982) constructed a theory of Hodge classes having many of the…