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Displaying similar documents to “The Chow ring of the stack of cyclic covers of the projective line”

A minimal Set of Generators for the Ring of multisymmetric Functions

David Rydh (2007)

Annales de l’institut Fourier

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The purpose of this article is to give, for any (commutative) ring A , an explicit minimal set of generators for the ring of multisymmetric functions T S A d ( A [ x 1 , ⋯ , x r ] ) = A [ x 1 , ⋯ , x r ] ⊗ A d 𝔖 d as an A -algebra. In characteristic zero, i.e. when A is a ℚ -algebra, a minimal set of generators has been known since the 19th century. A rather small generating set in the general case has also recently been given by Vaccarino but it is not minimal in general. We also give a sharp degree bound on the generators, improving...

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...

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,...

Quadratic Differentials and Equivariant Deformation Theory of Curves

Bernhard Köck, Aristides Kontogeorgis (2012)

Annales de l’institut Fourier

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Given a finite p -group G acting on a smooth projective curve X over an algebraically closed field k of characteristic p , the dimension of the tangent space of the associated equivariant deformation functor is equal to the dimension of the space of coinvariants of G acting on the space V of global holomorphic quadratic differentials on X . We apply known results about the Galois module structure of Riemann-Roch spaces to compute this dimension when G is cyclic or when the action of G on...

Computations with Witt vectors of length 3

Luís R. A. Finotti (2011)

Journal de Théorie des Nombres de Bordeaux

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In this paper we describe how to perform computations with Witt vectors of length 3 in an efficient way and give a formula that allows us to compute the third coordinate of the Greenberg transform of a polynomial directly. We apply these results to obtain information on the third coordinate of the j -invariant of the canonical lifting as a function on the j -invariant of the ordinary elliptic curve in characteristic p .