We prove results that, for a certain class of noncompact Calabi–Yau threefolds, relate the Frobenius action on their -adic cohomology to the Frobenius action on the -adic cohomology of the corresponding curves. In the Appendix, we describe our interpretation of the Griffiths–Dwork method.
REFERENCES
1.
Baldassarri
, F.
and D’Agnolo
, A.
, “On Dwork cohomology and algebraic D-modules
,” in Geometric Aspects of Dwork Theory
, Vols. I, II
, (Walter de Gruyter GmbH & Co. KG
, Berlin
, 2004
), pp. 245
–253
.2.
Candelas
, P.
, de la Ossa
, X.
, and Rodriguez Villegas
, F.
, “Calabi-Yau manifolds over finite fields. I.
,” e-print arXiv:hep-th/0012233.3.
Cox
, D. A.
and Katz
, S.
, Mirror Symmetry and Algebraic Geometry
, Mathematical Surveys and Monographs
Vol. 68
(American Mathematical Society
, Providence, RI
, 1999
).4.
Griffiths
, P.
, “On the periods of certain rational integrals. I.
,” Ann. Math.
90
, 460
(1969
).5.
Katz
, N. M.
, “On the differential equations satisfied by period matrices
,” Publ. Math., Inst. Hautes Etud. Sci.
35
, 71
(1968
).6.
Kontsevich
,M.
, Schwarz
,A.
, and Vologodsky
,V.
, “Integrality of instanton numbers and-adic B-model
,” Phys. Lett. B
637
, 97
(2006
);e-print arXiv:hep-th/0603106
7.
Schwarz
,A.
and Vologodsky
,V.
, “Frobenius transformation, mirror map and instanton numbers
,” Phys. Lett. B
660
, 422
(2008
);e-print arXiv:hep-th/0606151.
8.
Schwarz
, A.
and Vologodsky
, V.
, “Integrality theorems in the theory of topological strings
,” e-print arXiv:0807.1714.9.
Schwarz
, A.
and Shapiro
, I.
, “Twisted de Rham cohomology, homological definition of the integral and ‘Physics over a ring
,” e-print arXiv:0809.0086.10.
11.
© 2009 American Institute of Physics.
2009
American Institute of Physics
You do not currently have access to this content.
