  We provide a new condition for an absolutely almost simple algebraic group to
have good reduction with respect to a discrete valuation of the base field
which is formulated in terms of the existence of maximal tori with special
properties. This characterization, in particular, shows that the Finiteness
Conjecture for forms of an absolutely almost simple algebraic group over a
finitely generated field that have good reduction at a divisorial set of places
of the field would imply the finiteness of the genus of the group at hand. It
also leads to a new phenomenon that we refer to as "killing the genus by a
purely transcendental extension." Yet another application deals with the
investigation of "eigenvalue rigidity" of Zariski-dense subgroups, which in
turn is related to the analysis of length-commensurable Riemann surfaces and
general locally symmetric spaces. Finally, we analyze the Finiteness Conjecture
and the genus problem for simple algebraic groups of type $\textsf{F}_4$.
