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-Soule 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...
Modular Forms and Special Cycles on Shimura Curves is a thorough study of the generating functions constructed from special cycles, bot...
A monograph that treats one case of a series of conjectures by S Kudla, whose goal is to show that Fourier of Eisenstein series encode information about the Arakelov intersection theory of special cycles on Shimura varieties of orthogonal and unitary type.
A monograph that treats one case of a series of conjectures by S Kudla, whose goal is to show that Fourier of Eisenstein series encode information abo...
