TITLE: Constructing a degeneration (as a group scheme) of G_m to G_a
QUESTION [13 upvotes]: SGA 3, expose 12, remark 1.6 says that one can easily construct a group scheme over a discrete valuation ring with generic fiber Gm and special fiber Ga. 
What is such an example?

REPLY [14 votes]: One more point of view :   if X is a 2x2 matrix, its centralizer in PGL(2) is -- for generic X -- isomorphic to Gm; however, it is isomorphic to Ga if X is nonzero and nilpotent.  This gives a typical naturally occurring family (you can, of course, restrict it to get a family over a dvr).