Title of Paper: Invariant Theory and the Koszul Complex
Representations of Z/p in Characteristic p
Applications
Author: Larry Smith
AMS Code: 13A50 Invariant Theory
Address: Mathematisches Institut
Bunsenstrasse 3--5
D 37073 Goettingen
Federal republic of germany
e-mail: larry@sunrise.uni-math.gwdg.de
THIS IS a POstScript file.
Summary:
We study the ring of invariants $\F[V]^{\Z/p}$\/, and its derived functors
$H^i(\Z/p\semicolon \F[V])$\/, of the cyclic group $\Z/p$ of prime order
$p$ over
a field $\F$ of characteristic $p$\/. We verify a formula of Ellingsrud and
Skjelbred \cite{norway} for the homological codimension, show
the quotient algebra $\F[V]^{\Z/p}/\Im(\Tr^{\Z/p})$ is Cohen-Macaulay,
and that the ideal
generated by the elements in the image of the transfer homomorphism,
$\Im(\Tr^{\Z/p}) \subset \F[V]^{\Z/p}$\/, is primary of height $n-1$ when $V$
is an $n$-dimensional irreducible representation of $\Z/p$\/.
Using our cohomological computations and a previous result \cite{vectors}
about permutation representations we are able to obtain an upper bound for the
degree of homogeneous forms in a minimal algebra generating set for
$\F[V]^{\Z/p}$\/.