Displaying similar documents to “A minimal Set of Generators for the Ring of multisymmetric Functions”

Hasse–Schmidt derivations, divided powers and differential smoothness

Luis Narváez Macarro (2009)

Annales de l’institut Fourier

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Let k be a commutative ring, A a commutative k -algebra and D the filtered ring of k -linear differential operators of A . We prove that: (1) The graded ring gr D admits a canonical embedding θ into the graded dual of the symmetric algebra of the module Ω A / k of differentials of A over k , which has a canonical divided power structure. (2) There is a canonical morphism ϑ from the divided power algebra of the module of k -linear Hasse–Schmidt integrable derivations of A to gr D . (3) Morphisms θ and...

The higher transvectants are redundant

Abdelmalek Abdesselam, Jaydeep Chipalkatti (2009)

Annales de l’institut Fourier

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Let A , B denote generic binary forms, and let 𝔲 r = ( A , B ) r denote their r -th transvectant in the sense of classical invariant theory. In this paper we classify all the quadratic syzygies between the { 𝔲 r } . As a consequence, we show that each of the higher transvectants { 𝔲 r : r ≥ 2 } is redundant in the sense that it can be completely recovered from 𝔲 0 and 𝔲 1 . This result can be geometrically interpreted in terms of the incomplete Segre imbedding. The calculations rely upon the Cauchy exact sequence of S L 2 -representations,...

An explicit formula for the Hilbert symbol of a formal group

Floric Tavares Ribeiro (2011)

Annales de l’institut Fourier

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A Brückner-Vostokov formula for the Hilbert symbol of a formal group was established by Abrashkin under the assumption that roots of unity belong to the base field. The main motivation of this work is to remove this hypothesis. It is obtained by combining methods of ( ϕ , Γ )-modules and a cohomological interpretation of Abrashkin’s technique. To do this, we build ( ϕ , Γ )-modules adapted to the false Tate curve extension and generalize some related tools like the Herr complex with explicit formulas...

Which weakly ramified group actions admit a universal formal deformation?

Jakub Byszewski, Gunther Cornelissen (2009)

Annales de l’institut Fourier

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Consider a representation of a finite group G as automorphisms of a power series ring k [ [ t ] ] over a perfect field k of positive characteristic. Let D be the associated formal mixed-characteristic deformation functor. Assume that the action of G is weakly ramified, i.e., the second ramification group is trivial. Example: for a group action on an ordinary curve, the action of a ramification group on the completed local ring of any point is weakly ramified. ...

Ramification and moduli spaces of finite flat models

Naoki Imai (2011)

Annales de l’institut Fourier

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We determine the type of the zeta functions and the range of the dimensions of the moduli spaces of finite flat models of two-dimensional local Galois representations over finite fields. This gives a generalization of Raynaud’s theorem on the uniqueness of finite flat models in low ramifications.