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Modular forms and special cycles on shimura curves

By: Contributor(s): Material type: TextTextLanguage: English Series: Annals of mathemtics studies ; 161Publication details: Princeton Princeton University Press 2006Description: vii, 373pISBN:
  • 9780691125510 (PB)
Subject(s):
Contents:
Ch. 1. Introduction Ch. 2. Arithmetic intersection theory on stacks Ch. 3. Cycles on Shimura curves Ch. 4. An arithmetic theta function Ch. 5. The central derivative of a genus two Eisenstein series Ch. 6. The generating function for 0-cycles Ch. 6 App. The case p = 2,p.
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.
Item type: BOOKS
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IMSc Library 511.381 KUD (Browse shelf(Opens below)) Available 60124

Includes index

Includes bibliographical references

Ch. 1. Introduction Ch. 2. Arithmetic intersection theory on stacks Ch. 3. Cycles on Shimura curves Ch. 4. An arithmetic theta function Ch. 5. The central derivative of a genus two Eisenstein series Ch. 6. The generating function for 0-cycles Ch. 6 App. The case p = 2,p.

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.

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The Institute of Mathematical Sciences, Chennai, India