Related papers: Uniform bounds for obstructions to the integral Ta…

On a projective variety defined over a global field, any Brauer--Manin obstruction to the existence of rational points is captured by a finite subgroup of the Brauer group. We show that this subgroup can require arbitrarily many generators.

Let X be a separated scheme of finite type over an algebraically closed field k and let m be a natural number. By an explicit geometric construction using torsors we construct a pairing between the first mod m Suslin homology and the first…

We give evidence for a uniformization-type conjecture, that any algebraic variety can be altered into a variety endowed with a tower of smooth fibrations of relative dimension one.

While there exist now formulations of initial boundary value problems for Einstein's field equations which are well posed and preserve constraints and gauge conditions, the question of geometric uniqueness remains unresolved. For two…

Gaussian elimination answers any question about a finitely presented vector space. However, a "uniform family" of such presentations--given as generic relations among an unspecified number of generators--is susceptible to elimination only…

We prove for residually finite groups the following long standing conjecture: the number of twisted conjugacy classes of an automorphism of a finitely generated group is equal (if it is finite) to the number of finite dimensional…

In this paper, we are concerned with the BFV-reduction of first class constraints in classsical Hamiltonian mechanics and deformation quantization. As a result, we obtain continuous star products for certain singular reduced symplectic…

Suppose $X$ is a vector lattice and there is a notion of convergence $x_{\alpha} \rightarrow x$ in $X$. Then we can speak of an "unbounded" version of this convergence by saying that $(x_{\alpha})$ unbounded converges to $x\in X$ if $\lvert…

Conformal boundary conditions in two-dimensional conformal field theories are still mostly an uncharted territory. Even less is known about the relevant boundary deformations that connect them. A natural approach to the problem is via…

We introduce order conserving embeddings as a more general form of order preserving embeddings between finite dimensional nest algebras. The structure of these embeddings is determined, in terms of order indecomposable decompositions, and…

We study cohomological obstructions to equivariant unirationality, with special regard to actions of finite groups on del Pezzo surfaces and Fano threefolds.

Finite-order invariants of knots in arbitrary 3-manifolds (including non-orientable ones) are constructed and studied by methods of the topology of discriminant sets. Obstructions to the integrability of admissible weight systems to…

Several known constructions relate initial degenerations of projective toric varieties and Grassmannians to regular subdivisions of appropriate point configurations. We define a general framework which allows for partial generalizations of…

Separation bounds are a fundamental measure of the complexity of solving a zero-dimensional system as it measures how difficult it is to separate its zeroes. In the positive dimensional case, the notion of reach takes its place. In this…

A variety V is said to be coherent if any finitely generated subalgebra of a finitely presented member of V is finitely presented. It is shown here that V is coherent if and only if it satisfies a restricted form of uniform deductive…

Let $X$ be a smooth projective variety over a finitely generated field $K$ of characteristic~$0$ and fix an embedding $K \subset \mathbb{C}$. The Mumford--Tate conjecture is a precise way of saying that certain extra structure on the…

We introduce the notion of limiting theories, giving examples and providing a sufficient condition under which the first order theory of a structure is the limit of the first order theories of a collection of substructures. We also give a…

We develop a notion of limit for dagger categories, that we show is suitable in the following ways: it subsumes special cases known from the literature; dagger limits are unique up to unitary isomorphism; a wide class of dagger limits can…

For a family of varieties over a number field, we give conditions under which 100% of members have no Brauer-Manin obstruction to the Hasse principle.

We extend the theory of the universal eta-invariant to the case of relative bordism groups of manifolds with boundaries. This allows the construction of secondary descendants of the universal eta-invariant. We obtain an interpretation of…