Related papers: A model theory section conjecture

The purpose of the present paper is to make a mathematical study of the differences and relations among possible structures inherent in an object, as well as of the whole structure constituted by them (i.e., the structure of structures),…

We establish Grothendieck's section conjecture for an open subset of the Reichardt-Lind curve, and introduce the notion of a Brauer-Manin obstruction for sections of the fundamental group extension.

For the cluster category of a hereditary or a canonical algebra, equivalently for the cluster category of the hereditary category of coherent sheaves on a weighted projective line, we study the Grothendieck group with respect to an…

We conjecture the existence of a simple geometric structure underlying questions of reducibility of parabolically induced representations of reductive p-adic groups.

We reinterpret a result of Pop and Stix on the $p$-adic section conjecture in terms of Berkovich spaces and fixed points. In doing this, we see a version of the result extends to larger classes of fields, which in turn allows us to prove a…

A new category of algebro-geometric objects is defined. This construction is a vast generalization of existing F1-theories, as it contains the the theory of monoid schemes on the one hand and classical algebraic theory, e.g. Grothendieck…

Although contemporary model theory has been called "algebraic geometry minus fields", the formal methods of the two fields are radically different. This dissertation aims to shrink that gap by presenting a theory of logical schemes,…

On objects of a triangulated category with a stability condition, we construct a topology.

We propose a new approach to study plethysm coefficients by using the Schur-Weyl duality between the symmetric group and the partition algebra. This allows us to explain the stability properties of plethysm and Kronecker coefficients in a…

Let $R$ by a right coherent ring and $R$-Mod denote the category of left $R$-modules. We show that there is an abelian model structure on $R$-Mod whose cofibrant objects are precisely the Gorenstein flat modules. Employing a new method for…

We show that there is a model structure in the sense of Quillen on an arbitrary Frobenius category $\F$ such that the homotopy category of this model structure is equivalent to the stable category $\underline{\F}$ as triangulated…

We prove special cases of a general conjecture: If an invertible field theory admits a projectively topological boundary theory, then it has finite order in the abelian group of invertible field theories. One can substitute `gapped' for…

In this paper we introduce the notion of the stability of a sequence of modules over Hecke algebras. We prove that a finitely generated consistent sequence associated with Hecke algebras is representation stable.

We explore the canonical Grothendieck topology in some specific circumstances. First we use a description of the canonical topology to get a variant of Giraud's Theorem. Then we explore the canonical Grothendieck topology on the categories…

We establish a criterion for deciding whether a class of structures is the class of models of a geometric theory inside Grothendieck toposes; then we specialize this result to obtain a characterization of the infinitary first-order theories…

Translating notions and results from category theory to the theory of computability models of Longley and Normann, we introduce the Grothendieck computability model and the first-projection-simulation. We prove some basic properties of the…

We introduce global model categories as a general framework to capture several phenomena in global equivariant homotopy theory. We then construct genuine stabilizations of these, generalizing the usual passage from unstable to stable global…

We make available some results about model theory cyclically ordered groups. We start with a classification of complete theories of divisible abelian cyclically ordered groups. Then we look at the cyclically ordered groups where the only…

In this paper, we first introduce stable functors with respect to a preenveloping/precovering subcategory and investigate some of their properties. Using that we then introduce and study a relative complete cohomology theory in abelian…

Using Quillen-Lurie deformation theory formalism we develop an obstruction theory for studying the stable $\infty$-category of modules over a given geometric $\infty$-stack. The obstruction theory studies the problem of lifting compact…