algebraically closed fieldscharacteristic zerocomplex numbers structurescategoricity theorem/ C1160 Combinatorial mathematics C1110 Algebra C4210 Formal logicWe construct and study structures imitating the field of complex numbers with exponentiation. We give a natural, albeit non first-order, axiomatisation ...
In this paper, we prove that a pseudoexponential field has continuum many non-isomorphic countable real closed exponential subfields, each with an order preserving exponential map which is surjective onto the nonnegative elements. Indeed, this is true of any algebraically closed exponential field ...
Suslin, A.: On the K-theory of algebraically closed fields. Invent. Math. 73, 241–245 (1983) Article MATH MathSciNet Google Scholar Suslin, A., Voevodsky, V.: Singular homology of abstract algebraic varieties. Invent. Math. 123, 61–94 (1996) Article MATH MathSciNet Google Scholar...
We construct pseudo-elliptic bundles starting from a deformation datum defined over the function field of a curve over an algebraically closed field of positive characteristic. This leads us to study a variant of Dwork's accessary parameter problem. We give applications of our results to Galois ...
Perfect pseudo-algebraically closed fields are algebraically bounded - Chatzidakis, Hrushovski () Citation Context ...erstand definable sets of a theory, it is helpful to have invariants with nice properties. For a fixed pseudo-finite field K, there are two well-known invariants of definable ...
Let \\\(ilde K\\\) be an algebraically closed field and consider the ideal I generated by polynomials f 1 ,..., f m in \\\(ilde K\\\left[ {{X_1}, \\\ldots {X_n}} ight]\\\) . The Hilbert Nullstellensatz asserts that if I is not the whole ring, then f 1 ,...,...
Let F be an algebraically closed field of characteristic zero. In this paper we deal with matrix superalgebras (i.e. algebras graded by Z2, the cyclic group of order 2) endowed with a pseudoinvolution. The first goal is to present the classification of the pseudoinvolutions...
(x 1, ..., xn) we have p ≠ exp(g(x1, ..., xn)), then p has a root in K .;The second result is a proof that a special case of Shapiro's conjecture holds in pseudoexponential fields.;Theorem 2. Let K be an algebraically closed exponential field satisfying Schanuel's ...
Let $G$ be an affine algebraic group with a reductive identity component\n$G^{0}$ acting regularly on an affine Krull scheme $X = {Spec} (R)$ over an\nalgebraically closed field. Let $T$ be an algebraic subtorus of $G$ and suppose\nthat ${Q}(R)^{T}= {Q}(R^{T})$ of ...
Let \\(ilde{K}\\) be an algebraically closed field and consider the ideal I generated by polynomials f 1 ,…, f m in \\(ilde{K}[X_{1},\\ldots,X_{n}]\\) . The Hilbert Nullstellensatz asserts that if I is not the whole ring, then f 1 ,…, f m have a common \\(il...