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A note on extensions of algebraic and formal gorups I.

Noriyuki Suwa, Tsutomu Sekiguchi (1991)

Mathematische Zeitschrift

A note on extensions of algebraic and formal groups II.

Noriyuki Suwa, Tsutomu Sekiguchi (1994)

Mathematische Zeitschrift

A note on Frobenius divided modules in mixed characteristics

Pierre Berthelot (2012)

Bulletin de la Société Mathématique de France

If $X$ is a smooth scheme over a perfect field of characteristic $p$ , and if $𝒟_{X}^{(\infty)}$ is the sheaf of differential operators on $X$ [7], it is well known that giving an action of $𝒟_{X}^{(\infty)}$ on an $𝒪_{X}$ -module $ℰ$ is equivalent to giving an infinite sequence of $𝒪_{X}$ -modules descending $ℰ$ via the iterates of the Frobenius endomorphism of $X$ [5]. We show that this result can be generalized to any infinitesimal deformation $f : X \to S$ of a smooth morphism in characteristic $p$ , endowed with Frobenius liftings. We also show that it extends to adic...

A regularity criterion for semigroup rings.

Bruns, W., Gubeladze, J. (1999)

Georgian Mathematical Journal

An improved Briancon-Skoda theorem with applications to the Cohen-Macaulayness of Rees algebras.

Craig Huneke, Ian M. Aberbach (1993)

Mathematische Annalen

Autre Demonstration du theoreme Liant regularité et paltitude en caracteristique p.

Michel André (1994)

Manuscripta mathematica

Characteristic of Rings. Prime Fields

Christoph Schwarzweller, Artur Korniłowicz (2015)

Formalized Mathematics

The notion of the characteristic of rings and its basic properties are formalized [14], [39], [20]. Classification of prime fields in terms of isomorphisms with appropriate fields (ℚ or ℤ/p) are presented. To facilitate reasonings within the field of rational numbers, values of numerators and denominators of basic operations over rationals are computed.

Classe de conjugaison du frobenius des variétés abéliennes à réduction ordinaire

Rutger Noot (1995)

Annales de l'institut Fourier

Soient $X$ une variété abélienne sur un corps de nombres $E$ et $G$ son groupe de Mumford–Tate. Soit $v$ une valuation de $E$ et pour tout nombre premier $ℓ$ tel que $v (ℓ) = 0$ , soit $F_{ℓ} \in G (Q_{ℓ})$ l’automorphisme de Frobenius (géométrique) de la cohomologie étale $ℓ$ -adique de $X$ . On montre que si $X$ a une bonne réduction ordinaire en $v$ , alors il existe $F \in G (Q)$ tel que, pour tout $ℓ$ , $F_{ℓ}$ soit conjugué à $F$ dans $G (Q_{ℓ})$ . On montre un résultat analogue pour le frobenius de la cohomologie cristalline de la réduction de $X$ modulo $v$ .

Classification of projective surfaces with small sectional genus : char $p$ > $0$

M. Andreatta, E. Ballico (1990)

Rendiconti del Seminario Matematico della Università di Padova

Commutative rings with homomorphic power functions.

Dobbs, David E., Kiltinen, John O., Orndorff, Bobby J. (1992)

International Journal of Mathematics and Mathematical Sciences

Computations with Frobenius powers.

Hermiller, Susan, Swanson, Irena (2005)

Experimental Mathematics

Computing Hilbert-Kunz functions of 1-dimensional graded rings.

Kreuzer, Martin (2007)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

Conservation of the noetherianity by perfect transcendental field extensions.

Magdalena Fernández Lebrón, Luis Narváez Macarro (2003)

Revista Matemática Iberoamericana

Contracting endomorphisms and dualizing complexes

Saeed Nasseh, Sean Sather-Wagstaff (2015)

Czechoslovak Mathematical Journal

We investigate how one can detect the dualizing property for a chain complex over a commutative local Noetherian ring $R$ . Our focus is on homological properties of contracting endomorphisms of $R$ , e.g., the Frobenius endomorphism when $R$ contains a field of positive characteristic. For instance, in this case, when $R$ is $F$ -finite and $C$ is a semidualizing $R$ -complex, we prove that the following conditions are equivalent: (i) $C$ is a dualizing $R$ -complex; (ii) $C \sim 𝐑 {Hom}_{R} (^{n} R, C)$ for some $n > 0$ ; (iii) $G_{C} {-dim}^{n} R < \infty$ and $C$ is derived $𝐑 {Hom}_{R} (^{n} R, C)$ -reflexive...

Contraction par Frobenius de $G$ -modules

Michel Gros, Masaharu Kaneda (2011)

Annales de l’institut Fourier

Soit $G$ un groupe algébrique semi-simple simplement connexe défini sur un corps algébriquement clos $𝕜$ de caractéristique positive. Nous donnons une nouvelle preuve de l’existence d’un scindage de Frobenius de la variété des drapeaux de $G$ ainsi que de la nature $G$ -équivariante de celui-ci. L’outil principal est un scindage de l’endomorphisme de Frobenius défini sur toute l’algèbre des distributions de $G$ qui permet de « détordre » la structure des $G$ -modules.

Currently displaying 1 – 20 of 36