Periods of Hilbert Modular Surfaces

I. Hodge structures attached to primitive forms of weight 2. - 0. Definitions and notations. - 1. Hodge structures attached to Hilbert modular surfaces. - 2. Hodge structures attached to primitive forms of weight 2. - 3. Nonholomorphic involutive automorphisms of Hilbert modular surfaces. - 4. Period relation of Riemann-Hodge. - II. Abelian varieties attached to primitive forms. - 5. Abelian varieties attached to Clifford algebras. - 6. The period moduli of the isogeny classes Atf ? Q and A2f ? Q. - 7. Main theorem A and its corollaries. - 8. Selfconjugate forms and algebraic cycles. - 9. Abelian varieties attached to non-selfconjugate forms. - III. Correspondence between real Nebentype elliptic modular forms and Hilbert modular forms. - 10. Weil representation and theta series. - 11. Construction of real Nebentype elliptic modular forms. - 12. Construction of Hilbert modular forms. - 13. The adjointness formula. - IV. Period relation for the lifting of modular forms and transcendental cycles. - 14. Hodge structures attached to real Nebentype elliptic modular forms of weight 2. - 15. Construction of 2-cycles. - 16. Arithmetic index theorems. - 17. Period relation for the Doi-Naganuma lifting and Main Theorem B. - 18. Selfconjugate forms and transcendental cycles. - 19. Notes on ?-adic cohomology groups of certain Hilbert modular surfaces. - 20. Remarks. - Bibliography. Language: English