Related papers: On ordinary differentially large fields

We prove Grauert-Riemenschneider-type vanishing theorems for excellent dlt threefolds pairs whose closed points have perfect residue fields of positive characteristic $p>5$. Then we discuss applications to dlt singularities and to Mori…

In this note we study sets of NIP formulas in some theories of fields and valued fields, with a special focus on the sets of quantifier-free and existential formulas. First, we give a new proof of the fact that Separably Closed Valued…

We use a known example of an algebraically maximal discretely valued field of positive characteristic $p$ which admits purely inseparable extensions of degree $p^2$ with defect $p$ to construct algebraically maximal valued fields of…

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…

An $H$-field is a type of ordered valued differential field with a natural interaction between ordering, valuation, and derivation. The main examples are Hardy fields and fields of transseries. Aschenbrenner and van den Dries proved…

The paper deals with Henselian valued field with analytic structure. Actually, we are focused on separated analytic structures, but the results remain valid for strictly convergent analytic ones as well. A classical example of the latter is…

We offer an axiomatic definition of a differential algebra of generalized functions over an algebraically closed non-Archimedean field. This algebra is of {\em Colombeau type} in the sense that it contains a copy of the space of Schwartz…

Let $E$ be an algebraic extension of a global field $E_{0}$ with a nontrivial Brauer group Br$(E)$, and let $P(E)$ be the set of those prime numbers $p$, for which $E$ does not equal its maximal $p$-extension $E(p)$. This paper shows that…

Combining a characterisation by B\'elair, Kaplan, Scanlon and Wagner of certain $\rm NIP$ valued fields of characteristic $p$ with Dickson's construction of cyclic algebras, we provide examples of noncommutative $\rm NIP$ division ring of…

We consider the class of complete discretely valued fields such that the residue field is of prime characteristic p and the cardinality of a $p$-base is 1. This class includes two-dimensional local and local-global fields. A new definition…

We give model theoretic accounts and proofs of the existence and uniqueness of differential Galois extensions with no new constants, for logarithmic differential equations over a differential field K, when the field C of constants of K is…

Tangle-tree theorems are an important tool in structural graph theory, and abstract separation systems are a very general setting in which tangle-tree theorems can still be formulated and proven. For infinite abstract separation systems, so…

Motivated by the study of meromorphic vector fields, a model theory of "compact complex manifolds equipped with a generic derivation" is here proposed. This is made precise by the notion of a differential CCM-structure. A first-order…

This work is devoted to the study of the support of a Laurent series in several variables which is algebraic over the ring of power series over a characteristic zero field. Our first result is the existence of a kind of maximal dual cone of…

We show that there exists $k \in \bbn$ and $0 < \e \in\bbr$ such that for every field $F$ of characteristic zero and for every $n \in \bbn$, there exists explicitly given linear transformations $T_1,..., T_k: F^n \to F^n$ satisfying the…

This paper analyzes theorems about algebraic field extensions using the techniques of reverse mathematics. In section 2, we show that $\mathsf{WKL}_0$ is equivalent to the ability to extend $F$-automorphisms of field extensions to…

We study relative differential closure in the context of Hardy fields. Using our earlier work on algebraic differential equations over Hardy fields, this leads to a proof of a conjecture of Boshernitzan (1981): the intersection of all…

We show that any finite set S in a characteristic zero integral domain can be mapped to the finite field of order p, for infinitely many primes p, preserving all algebraic incidences in S. This can be seen as a generalization of the…

We find an infinite dimensional free algebra which lives at large N in any SU(N)-invariant action or Hamiltonian theory of bosonic matrices. The natural basis of this algebra is a free-algebraic generalization of Chebyshev polynomials and…

Let C be an algebraically closed field and X a projective curve over C. Consider an ordinary linear differential equation, or a linear differ- ence equation, with coefficients in the field of rational functions of X, and assume that its…