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Rational projectively Cohen-Macaulay surfaces of maximum degree.

Marina Mancini (2001)

Collectanea Mathematica

In this paper we determine the greatest degree of a rational projectively Cohen-Macaulay (p.C.M.) surface V in PN and we study the surfaces which attain such maximum degree.

Rational Puiseux expansions

Dominique Duval (1989)

Compositio Mathematica

Rational real algebraic models of topological surfaces.

Biswas, Indranil, Huisman, Johannes (2007)

Documenta Mathematica

Rational smoothness of varieties of representations for quivers of Dynkin type

Philippe Caldero, Ralf Schiffler (2004)

Annales de l’institut Fourier

We study the Zariski closures of orbits of representations of quivers of type $A$ , $D$ ou $E$ . With the help of Lusztig’s canonical base, we characterize the rationally smooth orbit closures and prove in particular that orbit closures are smooth if and only if they are rationally smooth.

Rational torsion points on elliptic curves over number fields

Bas Edixhoven (1993/1994)

Séminaire Bourbaki

Rational torsion points on Jacobians of modular curves

Hwajong Yoo (2016)

Acta Arithmetica

Let p be a prime greater than 3. Consider the modular curve X₀(3p) over ℚ and its Jacobian variety J₀(3p) over ℚ. Let (3p) and (3p) be the group of rational torsion points on J₀(3p) and the cuspidal group of J₀(3p), respectively. We prove that the 3-primary subgroups of (3p) and (3p) coincide unless p ≡ 1 (mod 9) and $3^{(p - 1) / 3} \equiv 1 (m o d p)$ .

Rationale Ausführung der Operationen in der Theorie der algebraischen Functionen.

Noether (1884)

Mathematische Annalen

Rationale Punkte auf Fermatkurven und getwisteten Modulkurven.

G. Frey (1982)

Journal für die reine und angewandte Mathematik

Rationale Punkte über eine algebraische Kurve (points rationnels sur une courbe algébrique)

Theodor Schneider (1973/1974)

Séminaire Delange-Pisot-Poitou. Théorie des nombres

Rationale Singularitäten komplexer Flächen.

E. BRIESKORN (1967/1968)

Inventiones mathematicae

Rationalité de valeurs spéciales de certaines fonctions L

Norbert SCHAPPACHER (1981/1982)

Seminaire de Théorie des Nombres de Bordeaux

Rationalité des fonctions $ζ$ des variétés algébriques

Jean-Pierre Serre (1958/1960)

Séminaire Bourbaki

Rationalité des Singularités Canoniques.

Renée Elkikj (1981)

Inventiones mathematicae

Rationalité et valeurs de fonctions $L$ en cohomologie cristalline

Jean-Yves Étesse (1988)

Annales de l'institut Fourier

Dans l’exposé Bourbaki 409, Katz conjecture la méromorphie $p$ -adique de la fonction $L (X, E, t)$ attachée à une variété $X$ lisse sur un corps fini $F_{q}$ ( $q = p^{a}$ ) et à un $F$ -cristal $E$ sur $X$ . Si $X$ est propre et lisse sur $F_{q}$ nous prouvons que $L$ est rationnelle et fournie par l’expression habituelle utilisant l’action du Frobenius sur la cohomologie cristalline à coefficients dans $E$ ; ce résultat n’était connu, via les “conjectures de Weil”, que pour des $F$ -cristaux unités particuliers: ceux provenant d’une représentation de...

Rationality of Moduli Spaces of Stable Bundles.

P.E.. Newstead (1975)

Mathematische Annalen

Rationality of Moduli spaces of torsion free sheaves over rational surfaces.

Lothar Göttsche (1996)

Manuscripta mathematica

Rationality of the moduli variety of curves of genus 3.

P. Katsylo (1996)

Commentarii mathematici Helvetici

Rationality of the quotient of ℙ2 by finite group of automorphisms over arbitrary field of characteristic zero

Andrey Trepalin (2014)

Open Mathematics

Let $𝕜$ be a field of characteristic zero and G be a finite group of automorphisms of projective plane over $𝕜$ . Castelnuovo’s criterion implies that the quotient of projective plane by G is rational if the field $𝕜$ is algebraically closed. In this paper we prove that $ℙ_{𝕜}^{2} / G$ is rational for an arbitrary field $𝕜$ of characteristic zero.

Rationally connected foliations on surfaces.

Neumann, Sebastian (2009)

Documenta Mathematica

Rationally connected varieties over local fields.

Kollár, János (1999)

Annals of Mathematics. Second Series

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