CM periods, CM regulators and hypergeometric functions, I

Abstract

We study the $H^2$ of certain surfaces with complex multiplication by a cyclotomic field. The periods are written in terms of values of the gamma function and the conjecture of Gross-Deligne is verified. The regulators of certain $K_1$-elements are written in terms of values of hypergeometric functions ${}_3{F}_2$, and we prove their non-vanishing.

33 pages

References in corpus (2)

• Periods of Hodge structures and special values of the gamma function
• Chern class and Riemann-Roch theorem for cohomology theory without homotopy invariance

Cited by in corpus (6)

• New p-adic hypergeometric functions and syntomic regulators
• An algebro-geometric study of special values of hypergeometric functions ${}_3{F}_2$
• F-isocrystal and syntomic regulators via hypergeometric functions
• Regulators of K_1 of Hypergeometric Fibrations
• Regulators of K_2 of Hypergeometric Fibrations
• A functional logarithmic formula for hypergeometric functions 3F2