Linear Source Modules and Trivial Source Modules

Robert Boltje
University of California, Santa Cruz
http://math.uscs.edu/~boltje

Abstract:
We consider the Grothendieck ring $L_\calO(G)$ of the
category of linear source $\calO G$-modules with respect to direct
sums, where $\calO$ is a complete discrete valuation ring of
characteristic zero containing enough roots of unity and having a
residue field of prime characteristic. We show that $L_\calO(G)$
is semisimple after tensoring with the field of fractions of
$\calO$, and we determine all its species. Moreover, we show that
there is a canonical integral induction formula for $L_\calO(G)$
inducing only lattices of rank 1. As a consequence we obtain
similar statements for the ring of trivial source $\calO
G$-modules.

Published in:
Proc. Sympos. Pure Math. 63 (1998), 7-30.