Doctor of Philosophy
Prof. Nicole Lemire and Prof. Eric Schost
The rationality problem for algebraic tori is well known. It is known that any algebraic torus is unirational over its field of definition. The first purpose of this work is to solve rationality problem for 5 dimensional stably rational algebraic tori with an indecomposable character lattice. In order to do so, we have studied the associated character lattices of the mentioned algebraic tori. For each character lattice L, either we see the lattice as an associated lattice to a root system (of which rationality of its corresponding algebraic torus is known) or we find a reduced component of L so that we can relate rationality of the associated algebraic torus to lower dimensions. Using these two main methods from , we solve rationality problem in some cases. The second problem of which we are concerned with here, is to give a constructive proof for the No Name Lemma.
Jamshidpey, Armin, "Algebraic Tori: A Computational Approach" (2017). Electronic Thesis and Dissertation Repository. 4692.