Anti-holomorphic multiplication and a real algebraic modular variety

Goresky, Mark; Tai, Yung sheng

doi:10.4310/jdg/1434052758

Cited by 3 publications

(2 citation statements)

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“…The Siegel space h n admits other interesting anti-holomorphic involutions. In [16] such an involution is described on h 2 whose fixed point set is hyperbolic 3-space (cf. [41]).…”

Section: The Complex Casementioning

confidence: 99%

“…15.3. In [16] the authors showed that certain arithmetic hyperbolic 3-manifolds (and more generally, certain arithmetic quotients of quaternionic Siegel space) can be viewed as parametrizing Abelian varieties with anti-holomorphic multiplication by the integers O d in a quadratic imaginary number field. It should be possible to mimic these constructions using Deligne modules.…”

Section: Proof the Proof Involves Two Steps First Associatingmentioning

confidence: 99%

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Real structures on ordinary Abelian varieties

Goresky¹,

Tai²

2017

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Contents 1. Introduction 2. The complex case 3. Deligne modules 4. q-inversive elements 5. Q-isogeny classes 6. Q-isogeny classes within a Q isogeny class 7. Isomorphism classes within a Q-isogeny class 8. Counting lattices 9. The Tate and Dieudonné modules 10. Polarization of the Dieudonné module 11. Real structures on the Dieudonné module 12. Basis of the Dieudonné module 13. Lattices in the Dieudonné module 14. The counting formula 15. Further questions Appendix A. Weil polynomials and a real counterpart Appendix B. Symplectic group Appendix C. Polarizations and positivity Appendix D. Involutions on the symplectic group Appendix E. Symplectic cohomology Appendix F. Finiteness Appendix G. Proof of Proposition 9.2 Appendix H. Involutions on the Witt vectors References

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“…The Siegel space h n admits other interesting anti-holomorphic involutions. In [16] such an involution is described on h 2 whose fixed point set is hyperbolic 3-space (cf. [41]).…”

Section: The Complex Casementioning

confidence: 99%

Section: Proof the Proof Involves Two Steps First Associatingmentioning

confidence: 99%