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We prove certain results comparing rationality of algebraic cycles over the function field of a quadric and over the base field. These results have already been obtained by Alexander Vishik in the case of characteristic 0, which allowed him to work with algebraic cobordism theory. Our proofs use the modulo 2 Steenrod operations in the Chow theory and work in any characteristic ≠ 2.

Around real Enriques surfaces.

Alexander Degtyarev, Vlatcheslav Kharlamov (1997)

Revista Matemática de la Universidad Complutense de Madrid

We present a brief overview of the classification of real Enriques surfaces completed recently and make an attempt to systemize the known classification results for other special types of surfaces. Emphasis is also given to the particular tools used and to the general phenomena discovered; in particular, we prove two new congruence type prohibitions on the Euler characteristic of the real part of a real algebraic surface.

Around the Gysin triangle. II.

Déglise, Frédéricke (2008)

Documenta Mathematica

Around the intersection form of an isolated singularity of hypersurface

D. Barlet, A. N. Varchenko (1988)

Compositio Mathematica

Arrangements d'hyperplans et sommes de Gauss

François Loeser (1991)

Annales scientifiques de l'École Normale Supérieure

Arrangements of lines and monodromy of plane curves

Mario Salvetti (1988)

Compositio Mathematica

Arrondissement des variétés à coins - Appendice à "Corners and Arithmetic Groups"

A. Douady, L. Hérault (1973)

Commentarii mathematici Helvetici

Artin Approximation and Formal Fibres of Local Rings.

Martin L. Brown (1983)

Mathematische Zeitschrift

Artin formalism and heat kernels.

Serge Lang, Jay Jorgenson (1994)

Journal für die reine und angewandte Mathematik

Artinian cofinite modules over complete Noetherian local rings

Behrouz Sadeghi, Kamal Bahmanpour, Jafar A'zami (2013)

Czechoslovak Mathematical Journal

Let $(R, 𝔪)$ be a complete Noetherian local ring, $I$ an ideal of $R$ and $M$ a nonzero Artinian $R$ -module. In this paper it is shown that if $𝔭$ is a prime ideal of $R$ such that $dim R / 𝔭 = 1$ and $(0 :_{M} 𝔭)$ is not finitely generated and for each $i \geq 2$ the $R$ -module ${Ext}_{R}^{i} (M, R / 𝔭)$ is of finite length, then the $R$ -module ${Ext}_{R}^{1} (M, R / 𝔭)$ is not of finite length. Using this result, it is shown that for all finitely generated $R$ -modules $N$ with $Supp (N) \subseteq V (I)$ and for all integers $i \geq 0$ , the $R$ -modules ${Ext}_{R}^{i} (N, M)$ are of finite length, if and only if, for all finitely generated $R$ -modules $N$ with $Supp (N) \subseteq V (I)$ and...

Artin-Large property for analytic manifolds of dimension two.

Ana Castilla (1994)

Mathematische Zeitschrift

Artin's Theorem on the Solutions of Analytic Equations in Positive Characteristic.

Michel André (1975)

Manuscripta mathematica

Artin-Schelter regular algebras of dimension five

Gunnar Fløystad, Jon Eivind Vatne (2011)

Banach Center Publications

We show that there are exactly three types of Hilbert series of Artin-Schelter regular algebras of dimension five with two generators. One of these cases (the most extreme) may not be realized by an enveloping algebra of a graded Lie algebra. This is a new phenomenon compared to lower dimensions, where all resolution types may be realized by such enveloping algebras.

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Arithmétique des courbes elliptiques et théorie d'Iwasawa

Arithmetisch definierte Gruppen mit Galoisoperation.

Arithmetisch ganze Differentiale der Modulfunktionenkörper 6. und 7. Stufe

Aritmética de los semigrupos de Arf y saturados. Aplicaciones.

Around rationality of cycles