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Length 2 variables of A[x,y] and transfer

Eric Edo, Stéphane Vénéreau (2001)

Annales Polonici Mathematici

We construct and study length 2 variables of A[x,y] (A is a commutative ring). If A is an integral domain, we determine among these variables those which are tame. If A is a UFD, we prove that these variables are all stably tame. We apply this construction to show that some polynomials of A[x₁,...,xₙ] are variables using transfer.

Les motifs de Tate et les opérateurs de périodicité de Connes

Abhishek Banerjee (2014)

Annales mathématiques Blaise Pascal

Dans cet article, nous définissons une catégorie M o t ˜ C des motifs sur une catégorie monoïdale symétrique ( C , ⊗ , 1 ) vérifiant certaines hypothèses. Le rôle des espaces sur ( C , ⊗ , 1 ) est joué par les monoïdes (non necessairement commutatifs) dans C . Pour définir les morphismes dans M o t ˜ C , nous utilisons des classes dans les groupes d’homologie cyclique bivariante. Le but est de montrer que les opérateurs de périodicité de Connes induisent des morphismes M ⊗ 𝕋 ⊗ 2 ⟶ M dans M o t ˜ C , où 𝕋 est le motif de Tate dans M o t ˜ C .

Lie description of higher obstructions to deforming submanifolds

Marco Manetti (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

To every morphism χ : L → M of differential graded Lie algebras we associate a functors of artin rings Def χ whose tangent and obstruction spaces are respectively the first and second cohomology group of the suspension of the mapping cone of χ . Such construction applies to Hilbert and Brill-Noether functors and allow to prove with ease that every higher obstruction to deforming a smooth submanifold of a Kähler manifold is annihilated by the semiregularity map.

Lifting D -modules from positive to zero characteristic

João Pedro P. dos Santos (2011)

Bulletin de la Société Mathématique de France

We study liftings or deformations of D -modules ( D is the ring of differential operators from EGA IV) from positive characteristic to characteristic zero using ideas of Matzat and Berthelot’s theory of arithmetic D -modules. We pay special attention to the growth of the differential Galois group of the liftings. We also apply formal deformation theory (following Schlessinger and Mazur) to analyze the space of all liftings of a given D -module in positive characteristic. At the end we compare the problems...

Lifting solutions over Galois rings.

Javier Gómez-Calderón (1990)

Extracta Mathematicae

In this note we generalize some results from finite fields to Galois rings which are finite extensions of the ring Zpm of integers modulo pm where p is a prime and m ≥ 1.

Lifting the field of norms

Laurent Berger (2014)

Journal de l’École polytechnique — Mathématiques

Let K be a finite extension of Q p . The field of norms of a p -adic Lie extension K ∞ / K is a local field of characteristic p which comes equipped with an action of Gal ( K ∞ / K ) . When can we lift this action to characteristic 0 , along with a compatible Frobenius map? In this note, we formulate precisely this question, explain its relevance to the theory of ( ϕ , Γ ) -modules, and give a condition for the existence of certain types of lifts.

Linear derivations with rings of constants generated by linear forms

Piotr Jędrzejewicz (2008)

Colloquium Mathematicae

Let k be a field. We describe all linear derivations d of the polynomial algebra k[x₁,...,xₘ] such that the algebra of constants with respect to d is generated by linear forms: (a) over k in the case of char k = 0, (b) over k [ x ₁ p , . . . , x ₘ p ] in the case of char k = p > 0.

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