Title: Variations on a Theroem of Haynes R. MIller and a Functor of Jean Lannes
Author: Larry Smith
AMS Codes: 55S10 Steenrod Algebra, 13A50 Invaraint Theory
Email: larry@sunrise.uni-math.gwdg.de
This is a PostScript file!!
Abstract: Recent advances in modular invariant theory have often made use of
Steenrod operations and the T-functor introduced by Jean Lannes. Many key
properties of this functor depend on a Theorem of Haynes Miller. These results
have been proved by a mixture of algebraic and topological methods for the full
algebra of cohomology operations, and hence are only proven for the
prime field F_p. Until now, for odd primes, it is not the algebra of cohomology
operations that enters invariant theory, but the subalgebra of reduced powers.
Deriving from the known results, those needed for invariant theory is sometimes
not so obvious. This is a technical manuscript, providing proofs,
over an arbitrary Galois field, of those key properties of unstable
algebras over the Steenrod algebra that are essential to modular invariant
theory. Being technical, it goes without saying that we
assume a familiarity with some version of the Steenrod algebra, be it
topological, as in the classical book of Steenrod and Epstein, or algebraic
as in my book Polynomial Invariants of Finite Groups, AK Peters Ltd. 1996.