Essential dimension of inseparable field extensions

Dimension of Difference Field Extensions

Multivariable Dimension Polynomials and New Invariants of Differential Field Extensions

We introduce a special type of reduction in the ring of differential polynomials and develop the appropriate technique of characteristic sets that allows to generalize the classical Kolchin’s theorem on differential dimension polynomial and find new differential birational invariants of a finitely generated differential field extension. 2000 Mathematics Subject Classification. 12H05, 12H20, 13N15.

Hopf Galois structures on primitive purely inseparable extensions

Let L/K be a primitive purely inseparable extension of fields of characteristic p, [L : K] > p, p odd. It is well known that L/K is Hopf Galois for some Hopf algebra H, and it is suspected that L/K is Hopf Galois for numerous choices of H. We construct a family of K-Hopf algebras H for which L is an H-Galois object. For some choices of K we will exhibit an infinite number of such H. We provide ...

Essential dimension

Informally speaking, the essential dimension of an algebraic object is the minimal number of independent parameters one needs to define it. This notion was initially introduced in the context where the objects in question are finite field extensions [BuR97]. Essential dimension has since been investigated in several broader contexts, by a range of techniques, and has been found to have interest...

Tori and essential dimension

The present paper deals with algebraic tori and essential dimension but in three unrelated contexts. After a recollection on essential dimension and generic torsors we explicitly construct a generic torsor for PGLn, n ≥ 5 odd. We also discuss the so called “tori method” which gives a geometric proof of a result of Ledet on the essential dimension of a cyclic group (see [4, 5]). In the last sect...