On a Rationality Problem for Fields of Cross-ratios

@article{Reichstein2020OnAR,
  title={On a Rationality Problem for Fields of Cross-ratios},
  author={Zinovy Reichstein},
  journal={Tokyo Journal of Mathematics},
  year={2020}
}
  • Z. Reichstein
  • Published 29 June 2018
  • Mathematics
  • Tokyo Journal of Mathematics
Let k be a field, x1, . . . , xn be independent variables and Ln = k(x1, . . . , xn). The symmetric group Σn acts on Ln by permuting the variables, and the projective linear group PGL2 acts by 
1 Citations
On a rationality problem for fields of cross-ratios II
Abstract Let k be a field, $x_1, \dots , x_n$ be independent variables and let $L_n = k(x_1, \dots , x_n)$ . The symmetric group $\operatorname {\Sigma }_n$ acts on $L_n$ by permuting theExpand

References

SHOWING 1-10 OF 18 REFERENCES
Division algebra coproducts of index n
Given a family of separable finite dimensional extensions {Li} of a field k, we construct a division algebra n2 over its center which is freely generated over k by the fields {Li} i.
The Noether Problem for spinor groups of small rank
Building on prior work of Bogomolov, Garibaldi, Guralnick, Igusa, Kordonskii, Merkurjev and others, we show that the Noether Problem for $\operatorname{Spin}_n$ has a positive solution for everyExpand
THE RATIONALITY PROBLEM FOR FORMS OF M
Let X be a del Pezzo surface of degree 5 defined over a field F . A theorem of Yu. I. Manin and P. Swinnerton-Dyer asserts that every Del Pezzo surface of degree 5 is rational. In this paper weExpand
GALOIS COHOMOLOGY
In these lectures, we give a very utilitarian description of the Galois cohomology needed in Wiles’ proof. For a more general approach, see any of the references. First we fix some notation. For aExpand
Essential dimension: A functorial point of view (After A. Merkurjev)
In these notes we develop a systematic study of the essential dimension of functors. This approach is due to A. Merkurjev and can be found in his unpublished notes [12]. The notion of essentialExpand
The Structure of Fields
In this chapter we shall analyze arbitrary extension fields of a given field. Since algebraic extensions were studied in some detail in Chapter V, the emphasis here will be on transcendentalExpand
Rational invariants for subgroups of S_5 and S_7
Let $G$ be a subgroup of $S_n$, the symmetric group of degree $n$. For any field $k$, $G$ acts naturally on the rational function field $k(x_1,x_2,\ldots,x_n)$ via $k$-automorphisms defined byExpand
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