Let k0 be a field of characteristic 0, and fix an algebraic closure k of k0. Let G be an algebraic k-group, and let Y be a G-k-variety. Let G0 be a k0-model (k0-form) of G. We ask whether Y admits a G0-equivariant k0-model. If Y admits a G- equivariant k0-model for...
Here we recall that an algebraic subvariety of S×DH is understood to be a component of an intersection (S×DH)∩V, where V is an algebraic subvariety of S×DˇH, where DˇH is the compact dual. References Cattani, E., Deligne, P., Kaplan, A.: On the locus of Hodge classes....
The possibility of such a proof and related results demonstrate fundamental differences between the concepts of real and algebraic closures of fields.doi:10.1016/0022-4049(91)90110-NTomas SanderJournal of Pure and Applied AlgebraT. Sander, "Existence and uniqueness of ...
Mathematics - Algebraic Geometry14Q1068W30In this paper we show that not all affine rational complex surfaces can be parametrized birationally and surjectively. For this purpose, we prove that, if S is an affine complex surface whose projective closure is smooth, a necessary condition for S to...
one wants to find an action of G wherein a prescribed element and its inverse have attracting points with large basins of attraction, and the rate of attraction is somewhat uniform.;Tits' alternative has it that if the Zariski closure of a finitely generated linear group Gamma is semisimple,...
F. Pixley, Polynomial interpolation and the Chinese remainder theorem for algebraic systems. Math. Z. 1975. Bd 143, N 3. 165-174. [2] P. Jeavons, D. Cohen, M. C. Cooper, Constraints, consistency and closure, Artificial Intelligence, vol. 101 (1998), pp. 251-265. [3] T. Feder,...
an assumed quasi-periodic solution is expanded in a multi-frequency Fourier series and the governing ordinary differential equations of the nonlinear system are projected onto a finite set of Fourier modes. The arising nonlinear algebraic system is then solved with, e.g., the Newton–Raphson iterat...
The results of Artin and Schreier [1926] on ordered fields, presented in Sections 1 and 2, extend known properties of R and C and give new insights into the relationship of a field to its algebraic closure. The remaining sections study valuations and completions, which have become valuable ...
Let $${\\mathcal{R}}$$ be an o-minimal expansion of a real closed field R, and K be the algebraic closure of R. In earlier papers we investigated the notions of $${\\mathcal{R}}$$ -definable K-holomorphic maps, K-analytic manifolds and their K-analytic subsets. We call such ...
A conjunction operation of satisfaction functions has the algebraic structure of the group. (b) Disjunction: |𝑥𝐹(𝑥)∨|𝑥𝐺(𝑥)|xF(x)∨|xG(x). Disjunction has the following properties: Closure: ∀𝐹,𝐺∈Φ⇒(|𝑥𝐹(𝑥)∨|𝑥𝐺(𝑥))∈|𝑥Φ(𝑥)∀F,G∈...