Related papers: On finite imaginaries

We study the projections in vector spaces over finite fields. We prove finite fields analogues of the bounds on the dimensions of the exceptional sets for Euclidean projection mapping. We provide examples which do not have exceptional…

In this paper, we prove weak elimination of imaginaries for perfect bounded pseudo-algebraically closed fields equipped with finitely many independent valuations. Our approach combines an extension result for types to invariant types with…

We classify the imaginaries in a large class of equicharacteristic zero henselian valued fields that contain all those with bounded inertia group, and more. To do so, we consider a mix of sorts introduced in earlier works of the two authors…

We give an example of an imaginary defined in certain valued fields with analytic structure which cannot be coded in the `geometric' sorts which suffice to code all imaginaries in the corresponding algebraic setting.

A slip on a paper concerning near-vector spaces is fixed. New characterization of near-vector spaces determined by finite fields is provided and the number (up to the isomorphism) of these spaces is exhibited.

We answer a question by Niederreiter concerning the enumeration of a class of subspaces of finite dimensional vector spaces over finite fields by proving a conjecture by Ghorpade and Ram.

An extension of algebras is a homomorphism of algebras preserving identities. We use extensions of algebras to study the finitistic dimension conjecture over Artin algebras. Let $f: B \to A$ be an extension of Artin algebras. We denote by…

We use a generalization of a construction by Ziegler to show that for any field $F$ and any countable collection of countable subsets $A_i \subseteq F, i \in \calI \subset \Z_{>0}$ there exist infinitely many fields $K$ of arbitrary…

Let $T$ be a first-order theory. A correspondence is established between internal covers of models of $T$ and definable groupoids within $T$. We also consider amalgamations of independent diagrams of algebraically closed substructures, and…

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…

We study infinite groups interpretable in three families of valued fields: $V$-minimal, power bounded $T$-convex, and $p$-adically closed fields. We show that every such group $G$ has unbounded exponent and that if $G$ is dp-minimal then it…

We prove extension-dimensional versions of finite dimensional selection and approximation theorems. As applications, we obtain several results on extension dimension.

We construct an infinite family of imaginary quadratic number fields with 2-class groups of type (2,2,2) whose Hilbert 2-class fields are finite.

We show that separably closed valued fields of finite imperfection degree (either with lambda-functions or commuting Hasse derivations) eliminate imaginaries in the geometric language. We then use this classification of interpretable sets…

We prove finiteness results on integral points on complements of large divisors in projective varieties over finitely generated fields of characteristic zero. To do so, we prove a function field analogue of arithmetic finiteness results of…

We construct and study fields F with the property that F has infinitely many extensions of some fixed degree, but E*/(E*)^n is finite for every finite extension E of F and every n>0.

The finitistic dimension conjecture asserts that any finite-dimensional algebra over a field should have finite finitistic dimension. Recently, this conjecture is reduced to studying finitistic dimensions for extensions of algebras. In this…

We formulate and analyze several finiteness conjectures for linear algebraic groups over higher-dimensional fields. In fact, we prove all of these conjectures for algebraic tori as well as in some other situations. This work relies in an…

We introduce new motivic invariants of arbitrary varieties over a perfect field. These cohomological invariants take values in the category of one-motives (considered up to isogeny in positive characteristic). The algebraic definition of…

We prove the dp-finite case of the Shelah conjecture on NIP fields. If K is a dp-finite field, then K admits a non-trivial definable henselian valuation ring, unless K is finite, real closed, or algebraically closed. As a consequence, the…