We prove results that, for a certain class of noncompact Calabi–Yau threefolds, relate the Frobenius action on their p-adic cohomology to the Frobenius action on the p-adic cohomology of the corresponding curves. In the  Appendix, we describe our interpretation of the Griffiths–Dwork method.

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 andp-adic B-model
,”
Phys. Lett. B
637
,
97
(
2006
);
7.
Schwarz
,
A.
and
Vologodsky
,
V.
, “
Frobenius transformation, mirror map and instanton numbers
,”
Phys. Lett. B
660
,
422
(
2008
);
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.
Shapiro
,
I.
, “
Frobenius map for quintic threefolds
,” e-print arXiv:0809.3742.
11.
Vologodsky
,
V.
, “
Integrality of instanton numbers
,” e-print arXiv:0707.4617.
You do not currently have access to this content.