Modular Forms and Special Cycles on Shimura Curves. (AM-161)

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Modular Forms and Special Cycles on Shimura Curves. (AM-161) Description

"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 Siegel-Weil formula identifies the generating function for zero-cycles as the central derivative of a Siegel Eisenstein [Read more...]

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