Modular forms and special cycles on Shimura curves (AM-161)

Modular Forms and Special Cycles on Shimura Curves is a thorough study of the generating functions constructed from special cycles, both divisors and zero-cycles, on the arithmetic surface ""M"" attached to a Shimura curve ""M"" over the field of rational numbers. These generating functions are shown to be the q-expansions of modular forms and Siegel modular forms of genus two respectively, valued in the Gillet-Soulé arithmetic Chow groups of ""M"". The two types of generating functions are related via an arithmetic inner product formula. In addition, an analogue of the classical Siegel-Weil