Modular Forms and Special Cycles on Shimura Curves AM 161 is popular PDF and ePub book, written by Stephen S. Kudla in 2006-04-24, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Modular Forms and Special Cycles on Shimura Curves AM 161 can be Read Online from any device for your convenience.
Modular Forms and Special Cycles on Shimura Curves AM 161 Book PDF Summary
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 formula identifies the generating function for zero-cycles as the central derivative of a Siegel Eisenstein series. As an application, an arithmetic analogue of the Shimura-Waldspurger correspondence is constructed, carrying holomorphic cusp forms of weight 3/2 to classes in the Mordell-Weil group of "M". In certain cases, the nonvanishing of this correspondence is related to the central derivative of the standard L-function for a modular form of weight 2. These results depend on a novel mixture of modular forms and arithmetic geometry and should provide a paradigm for further investigations. The proofs involve a wide range of techniques, including arithmetic intersection theory, the arithmetic adjunction formula, representation densities of quadratic forms, deformation theory of p-divisible groups, p-adic uniformization, the Weil representation, the local and global theta correspondence, and the doubling integral representation of L-functions.
Detail Book of Modular Forms and Special Cycles on Shimura Curves AM 161 PDF
- Author : Stephen S. Kudla
- Release : 24 April 2006
- Publisher : Princeton University Press
- ISBN : 9780691125510
- Genre : Mathematics
- Total Page : 387 pages
- Language : English
- PDF File Size : 10,7 Mb
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