Hermitian forms over local orders : an injectivity result
by
Laura Fainsilber
Göteborg University and Chalmers Tekniska Högskola
Coauthors: Jorge Morales (LSU, Baton Rouge)

Let L be a ring endowed with an involution a --> a'. We say that two units a and b of L fixed under the involution are congruent if there is an element u in L^× such that a = u b u'.

The set of congruence classes H(L) then corresponds to a set of isometry classes of hermitian forms.

We consider the case where L is an order with involution in a semisimple algebra A over a local field and study the question whether the natural map H(L) --> H(A) induced by inclusion is injective.

We give sufficient conditions on the order L for this map to be injective (for instance that L be hereditary).

We give applications to hermitian forms over group rings and G-hermitian forms over local rings for certain finite groups G, not necessarily abelian.

Date received: April 13, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacf-29.