7,247 research outputs found
The compatibility with the duality for partial Hasse invariants
We give a simple and natural proof for the compatibility of the Hasse
invariant with duality. We then study a -divisible group with an action of
the ring of integers of a finite ramified extension of . We
suppose that it satisfies the Pappas-Rapoport condition ; in that case the
Hasse invariant is a product of partial Hasse invariants, each of which can be
expressed in terms of primitive Hasse invariants. We then show that the dual of
the -divisible group naturally satisfies a Pappas-Rapoport condition, and
prove the compatibility with the duality for the partial and primitive Hasse
invariants.Comment: 12 page
Homomorphic Data Isolation for Hardware Trojan Protection
The interest in homomorphic encryption/decryption is increasing due to its
excellent security properties and operating facilities. It allows operating on
data without revealing its content. In this work, we suggest using homomorphism
for Hardware Trojan protection. We implement two partial homomorphic designs
based on ElGamal encryption/decryption scheme. The first design is a
multiplicative homomorphic, whereas the second one is an additive homomorphic.
We implement the proposed designs on a low-cost Xilinx Spartan-6 FPGA. Area
utilization, delay, and power consumption are reported for both designs.
Furthermore, we introduce a dual-circuit design that combines the two earlier
designs using resource sharing in order to have minimum area cost. Experimental
results show that our dual-circuit design saves 35% of the logic resources
compared to a regular design without resource sharing. The saving in power
consumption is 20%, whereas the number of cycles needed remains almost the sam
On ring class eigenspaces of Mordell-Weil groups of elliptic curves over global function fields
If E is a non-isotrivial elliptic curve over a global function field F of odd
characteristic we show that certain Mordell-Weil groups of E have 1-dimensional
eigenspace relative to a fixed complex ring class character provided that the
projection onto this eigenspace of a suitable Drinfeld-Heegner point is
nonzero. This represents the analogue in the function field setting of a
theorem for rational elliptic curves due to Bertolini and Darmon, and at the
same time is a generalization of the main result proved by Brown in his
monograph on Heegner modules. As in the number field case, our proof employs
Kolyvagin-type arguments, and the cohomological machinery is started up by the
control on the Galois structure of the torsion of E provided by classical
results of Igusa in positive characteristic.Comment: 20 pages, to appear in J. Number Theor
Modular symbols in Iwasawa theory
This survey paper is focused on a connection between the geometry of
and the arithmetic of over global fields,
for integers . For over , there is an explicit
conjecture of the third author relating the geometry of modular curves and the
arithmetic of cyclotomic fields, and it is proven in many instances by the work
of the first two authors. The paper is divided into three parts: in the first,
we explain the conjecture of the third author and the main result of the first
two authors on it. In the second, we explain an analogous conjecture and result
for over . In the third, we pose questions for general
over the rationals, imaginary quadratic fields, and global function fields.Comment: 43 page
Complex Multiplication Symmetry of Black Hole Attractors
We show how Moore's observation, in the context of toroidal compactifications
in type IIB string theory, concerning the complex multiplication structure of
black hole attractor varieties, can be generalized to Calabi-Yau
compactifications with finite fundamental groups. This generalization leads to
an alternative general framework in terms of motives associated to a Calabi-Yau
variety in which it is possible to address the arithmetic nature of the
attractor varieties in a universal way via Deligne's period conjecture.Comment: 28 page
Class groups and local indecomposability for non-CM forms
In the late 1990's, R. Coleman and R. Greenberg (independently) asked for a
global property characterizing those -ordinary cuspidal eigenforms whose
associated Galois representation becomes decomposable upon restriction to a
decomposition group at . It is expected that such -ordinary eigenforms
are precisely those with complex multiplication. In this paper, we study
Coleman-Greenberg's question using Galois deformation theory. In particular,
for -ordinary eigenforms which are congruent to one with complex
multiplication, we prove that the conjectured answer follows from the
-indivisibility of a certain class group.Comment: 40 pages, with a 11-page appendix by Haruzo Hida. v3: improvements to
exposition, minor correction
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