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Showing 1 to 9 of 9 for “"Algebraic closure"”.
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Algebraically closed fields with characters; differential-henselian monotone valued differential fields
… the 2-sorted structure (F, C; χ), where F is an algebraic closure of a finite field of characteristic p, C is the field of complex numbers and χ ∶ F → C is an injective, multiplication preserving map. In the second project we study the model theory of the differential-henselian monotone valued …
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The Absolute Galois Group of the Rationals, Grothendieck's Dessin D'Enfants, and Galois Invariants
… equivalence between the category of irreducible algebraic curves over the algebraic closure of the rationals and the category of finite covers of the Riemann sphere ramified at three points. We observe that the latter is also equivalent to the category of A. Grothendieck's dessins d'enfants: …
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Ideal Membership in Polynomial Rings Over the Integers
… of the restricted p-adic power series which are algebraic over Z [X]. Here, we make extensive use of a height function on the algebraic closure of Q (X) introduced by Kani (1978). Among other things, we obtain an effective version of the Weierstrass Division Theorem for the ring Z …
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RATIONAL POINTS ON SOME FAMILIES OF ELLIPTIC CURVES
… Q(t) in these cases. (Here Qbar represents the algebraic closure of Q.) All quadratic polynomials m(t) are classified by whether or not E_m(t) contains an additional rational point of low degree. Results similar to these are also obtained for other families of elliptic curves.
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Modest Automorphisms of Presburger Arithmetic
… results to describe the definable sets and algebraic closure of the quotient structure and Presburger structure expanded by the first automorphism. This allows us in Chapter 8 to show that the DP-rank in both cases is 2. Finally, in the concluding chapter, we describe some areas of possible …
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Large eddy simulation of premixed combustion using flamelets
… Two models are identified, one based on an algebraic expression for the reaction rate of a progress variable and the assumption of fast chemistry, the other based on a database of unstrained flamelets in which reaction rates are stored and parametrised using a progress variable and its SGS …
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WEIGHT STRUCTURES AND MOTIVIC COMPARISONS OF P-ADIC COHOMOLOGY THEORIES FOR RIGID ANALYTIC SPACES
… rigid analytic spaces over C_p, the completed algebraic closure of Q_p. Specifically, we prove that, for adic étale motives over C_p, the vector bundles on the Fargues--Fontaine curve arising from their Hyodo--Kato cohomology coincide with their de Rham--Fargues--Fontaine cohomology. The …
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Three applications of the regularity method in combinatorics
… that no pair of eigenvalues of 𝑀₁𝑀₂⁻¹ (over the algebraic closure [notation]) are negatives of each other. In particular, the “rotated squares” pattern does not satisfy this eigenvalue condition, and we give a construction of a set of positive density in [notation] for which that pattern has no …
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Contributions to model theory of metric structures
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