Section:
New Results
Towards a function field version of Freiman's theorem
In a collaboration with Christine Bachoc and Gilles Zémor (University
of Bordeaux), A. Couvreur obtained a characterisation of subspaces
of a function field over an algebraically closed field
satisfiying
where denotes the space spanned by all the products of two
elements of . They obtained the following result [18]:
Theorem.
Let be a function field over an algebraically closed field,
and be a finite dimensional subspace of which
spans as an algebra and such that
Then is a function field of transcendence degree 1 and