1-Motives with Torsion and Cartier Duality Park, Donghoon creator 2009 vi, 81 p. born digital Thesis (Ph.D.) -- Brown University (2009) Lichtenbaum, Stephen director Lichtenbaum, Stephen reader Goncharov, Alexander reader Rosen, Michael reader Brown University. Mathematics sponsor theses We define a category of smooth 1-motives with torsion over a locally noetherian base scheme and prove its Cartier duality. More precisely, we prove that the category of smooth 1-motives with torsion is equivalent to the category trivializations of particular biextensions, and this implies the Cartier duality for smooth 1-motives with torsion. We also show that this category has realization functors when the base scheme is a spectrum of a field. Cartier duality theorem was already proved in the case of 1-motives over a field by Deligne or Ramachandran. We will extend this result to any locally noetherian base scheme and moreover to 1-motives with torsion. The category of smooth 1-motives with torsion is not an abelian cateogory, but there are many realization functors as the category of 1-motives. smooth 1-motives with torsion Cartier duality RPB 20091218 engEnglish10.7301/Z0GQ6W14In CopyrightCollection is open for research.dissertations