The Inverse Invariant Theory Problem and Steenrod Operations
Mara D Neusel
AMS Classification: 55S10 Steenrod Algebra, 13A50 Invariant Theory, 55XX Algebraic Topology
AG Invariantentheorie
mdn@sunrise.uni-math.gwdg.de
This is a pure postscript file.
This is a (heavily) revised version of the paper with the same
titel put on Hopf in June. I have corrected some blunders
and at least 1001 typos, added more examples and
rewritten big parts of the story. I hope it is now more readable.
Here the original abstract once more:
This paper is devoted to the study of inverse
invariant theory and its relationship with the $\steenrod$--invariant
prime spectrum of an unstable algebra over the Steenrod algebra.
We will show that this spectrum is a chain saturated poset.
Moreover we will prove the existence of Thom classes, detect a
fractal of the Dickson algebra in any unstable algebra and give a counterexample
to the Reverse Landweber--Stong Conjecture.
Along the way to these results we will generalize the famous Adams--Wilkerson
theorems to arbitrary Galois fields, have a closer look at
fields and their extensions over the Steenrod algebra, and generalize
some results about the unstable part of a module over
the Steenrod algebra.