Related papers: A note on the effective listing of complete types

We determine when an arithmetic subgroup of a reductive group defined over a global function field is of type FP_\infty by comparing its large-scale geometry to the large-scale geometry of lattices in real semisimple Lie groups.

We show that the mathematical meaning of working in characteristic one is directly connected to the fields of idempotent analysis and tropical algebraic geometry and we relate this idea to the notion of the absolute point. After introducing…

Let k be a an algebraically closed field of arbitrary characteristic, and we let h be the usual Weil height for the n-dimensional affine space corresponding to the function field k(t) (extended to its algebraic closure). We prove that for…

We give the classification of thick representations and dense representations of the symmetric group over a field of characteristic zero.

We classify Artin-Schreier extensions of valued fields with non-trivial defect according to whether they are connected with purely inseparable extensions with non-trivial defect, or not. We use this classification to show that in positive…

We use the recently introduced \'etale open topology to prove several facts about large fields. We show that these facts lift to a very general topological setting.

In this expository article, the real numbers are defined as infinite decimals. After defining an ordering relation and the arithmetic operations, it is shown that the set of real numbers is a complete ordered field. It is further shown that…

We elaborate on a recently proposed geometric framework for scalar effective field theories. Starting from the action, a metric can be identified that enables the construction of geometric quantities on the associated functional manifold.…

We derive an effective field theory for general chaotic two-dimensional conformal field theories with a large central charge. The theory is a specific and calculable instance of a more general framework recently proposed in [1]. We discuss…

Characteristic integrals of Toda field theories associated to simple Lie algebras are presented in the most explicit forms, both in terms of the formulas and in terms of the proofs.

In the present paper we use the theory of exact completions to study categorical properties of small setoids in Martin-L\"of type theory and, more generally, of models of the Constructive Elementary Theory of the Category of Sets, in terms…

We begin the study of completeness of affine connections, especially those on statistical manifolds as well as on affine hypersurfaces. We collect basic facts, prove new theorems and provide examples with remarkable properties.

We examine categoricity issues for computable algebraic fields. We give a structural criterion for relative computable categoricity of these fields, and use it to construct a field that is computably categorical, but not relatively…

It is shown that the characteristic classes of foliations that were defined by Losik and that take values in the de~Rham cohomology of the space of infinite order frames over the leaf space may be mapped to the characteristic classes with…

We obtain a Bogomolov type of result for the additive group scheme in characteristic $p$. Our result is equivalent with a Bogomolov theorem for Drinfeld modules defined over a finite field.

We give a characterization of finitely ramified $\omega$-pseudo complete valued fields of mixed characteristic $(0, p)$, with fixed residue field $k$ and value group $G$ of cardinality $\aleph_{1}$, in terms of a Hahn-like construction over…

In our previous paper entitled "Axiomatic differential geometry -towards model categories of differential geometry-, we have given a category-theoretic framework of differential geometry. As the first part of our series of papers concerned…

We develop a theory of integration over valued fields of residue characteristic zero. In particular we obtain new and base-field independent foundations for integration over local fields of large residue characteristic, extending results of…

In this thesis three topics on the model theory of partial differential fields are considered: the generalized Galois theory for partial differential fields, geometric axioms for the theory of partial differentially closed fields, and the…

We develop a general theory of extensions of flat functors along geometric morphisms of toposes, and apply it to the study of the class of theories whose classifying topos is equivalent to a presheaf topos. As a result, we obtain a…