Related papers: Quantifier elimination on some pseudo-algebraicall…
We classify all cubic function fields over any finite field, particularly developing a complete Galois theory which includes those cases when the constant field is missing certain roots of unity. In doing so, we find criteria which allow…
Pseudo algebraically closed, pseudo real closed, and pseudo $p$-adically closed fields are examples of unstable fields that share many similarities, but have mostly been studied separately. In this text, we propose a unified framework for…
We study the Galois symbol map associated to the multiplicative group and an abelian variety which has good ordinary reduction over a $p$-adic field. As a byproduct, one can calculate the "class group" in the view of the class field theory…
We establish relative quantifier elimination for valued fields of residue characteristic zero enriched with a non-surjective valued field endomorphism, building on recent work of Dor and Halevi. In particular, we deduce relative quantifier…
We extend projectively equivariant quantization and symbol calculus to symbols of pseudo-differential operators. An explicit expression in terms of hypergeometric functions with noncommutative arguments is given. Some examples are worked…
The aim of this work is to develop a global calculus for pseudo-differential operators acting on suitable algebras of generalized functions. In particular, a condition of global hypoellipticity of the symbols gives a result of regularity…
We introduce a new type of closure operator on the set of relations, max-implementation, and its weaker analog max-quantification. Then we show that approximation preserving reductions between counting constraint satisfaction problems…
In their paper 'p-adic and real subanalytic sets, J. Denef and L. van den Dries prove that the theory of the ring of p-adic integers admits the elimination of quantifiers in the language of p-adic restricted analytic functions expanded by a…
We give a sufficient condition for a model theoretic structure $B$ to 'inherit' quantifier elimination from another structure $A$. This yields an alternative proof of one of the main result from \cite{kle}, namely quantifier elimination for…
Semifields are semirings in which every nonzero element has a multiplicative inverse. A rough classification uses the characteristic of the semifield, that is the isomorphism type of the semifield generated by the two neutral elements. For…
We present a logical separability analysis for a functional quantum computation language. This logic is inspired by previous works on logical analysis of aliasing for imperative functional programs. Both analyses share similarities notably…
Recent improvement on Tarski's procedure for quantifier elimination in the first order theory of real numbers makes it feasible to solve small instances of the following problems completely automatically: 1. listing all equality and…
Algebraic geometrical concepts are playing an increasing role in quantum applications such as coding, cryptography, tomography and computing. We point out here the prominent role played by Galois fields viewed as cyclotomic extensions of…
Admitting a non-trivial $p$-henselian valuation is a weaker assumption on a field than admitting a non-trivial henselian valuation. Unlike henselianity, $p$-henselianity is an elementary property in the language of rings. We are interested…
Relations and isomorphisms between quantum field theories in operator and functional integral formalisms are analyzed from the viewpoint of inequivalent representations of commutator or anticommutator rings of field operators. A functional…
No type II$_1$ tracial von Neumann algebra has theory that admits quantifier elimination.
In this exposition we discuss the theory of algebraic extensions of valued fields. Our approach is mostly through Galois theory. Most of the results are well-known, but some are new. No previous knowledge on the theory of valuations is…
Let D be a valued division algebra, finite-dimensional over its center F. Assume D has an unramified splitting field. The paper shows that if D contains a maximal subfield which is Galois over F (i.e. D is a crossed product) then the…
We present closed forms for several functions that are fundamental in number theory and we explain the method used to obtain them. Concretely, we find formulas for the p-adic valuation, the number-of-divisors function, the sum-of-divisors…
Algebraic quantum field theory provides a general, mathematically precise description of the structure of quantum field theories, and then draws out consequences of this structure by means of various mathematical tools -- the theory of…