224 research outputs found
Endomorphisms of superelliptic jacobians
Let K be a field of characteristic zero, n>4 an integer, f(x) an irreducible
polynomial over K of degree n, whose Galois group is doubly transitive simple
non-abelian group. Let p be an odd prime, Z[\zeta_p] the ring of integers in
the p-th cyclotomic field,
C_{f,p}:y^p=f(x) the corresponding superelliptic curve and J(C_{f,p}) its
jacobian. Assuming that either n=p+1 or p does not divide n(n-1), we prove that
the ring of all endomorphisms of J(C_{f,p}) coincides with Z[\zeta_p].Comment: Several typos have been correcte
Numerical evidence toward a 2-adic equivariant ''Main Conjecture''
International audienceWe test a conjectural non abelian refinement of the classical 2-adic Main Conjecture of Iwasawa theory. In the first part, we show how, in the special case that we study, the validity of this refinement is equivalent to a congruence condition on the coefficients of some power series. Then, in the second part, we explain how to compute the first coefficients of this power series and thus numerically check the conjecture in that setting
Completed cohomology of Shimura curves and a p-adic Jacquet-Langlands correspondence
We study indefinite quaternion algebras over totally real fields F, and give
an example of a cohomological construction of p-adic Jacquet-Langlands
functoriality using completed cohomology. We also study the (tame) levels of
p-adic automorphic forms on these quaternion algebras and give an analogue of
Mazur's `level lowering' principle.Comment: Updated version. Contains some minor corrections compared to the
published versio
Encoding multistate charge order and chirality in endotaxial heterostructures
Intrinsic resistivity changes associated with charge density wave (CDW) phase
transitions in 1T-TaS hold promise for non-volatile memory and computing
devices based on the principle of phase change memory (PCM). High-density PCM
storage is proposed for materials with multiple intermediate resistance states,
which have been observed in 1T-TaS. However, the metastability responsible
for this behavior makes the presence of multistate switching unpredictable in
1T-TaS devices. Here, we demonstrate the synthesis of nanothick
verti-lateral 1H-TaS/1T-TaS heterostructures in which the number of
endotaxial metallic 1H-TaS monolayers dictates the number of
high-temperature resistance transitions in 1T-TaS lamellae. Further, we
also observe optically active heterochirality in the CDW superlattice
structure, which is modulated in concert with the resistivity steps. This
thermally-induced polytype conversion nucleates at folds and kinks where
interlayer translations that relax local strain favorably align 1H and 1T
layers. This work positions endotaxial TaS heterostructures as prime
candidates for non-volatile device schemes implementing coupled switching of
structure, chirality, and resistance
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
Denominators of Eisenstein cohomology classes for GL_2 over imaginary quadratic fields
We study the arithmetic of Eisenstein cohomology classes (in the sense of G.
Harder) for symmetric spaces associated to GL_2 over imaginary quadratic
fields. We prove in many cases a lower bound on their denominator in terms of a
special L-value of a Hecke character providing evidence for a conjecture of
Harder that the denominator is given by this L-value. We also prove under some
additional assumptions that the restriction of the classes to the boundary of
the Borel-Serre compactification of the spaces is integral. Such classes are
interesting for their use in congruences with cuspidal classes to prove
connections between the special L-value and the size of the Selmer group of the
Hecke character.Comment: 37 pages; strengthened integrality result (Proposition 16), corrected
statement of Theorem 3, and revised introductio
Endomorphism algebras of Abelian varieties with special reference to superelliptic Jacobians
This is (mostly) a survey article. We use an information about Galois properties of points of small order on an Abelian variety in order to describe its endomorphism algebra over an algebraic closure of the ground field. We discuss in detail applications to jacobians of cyclic covers of the projective line
Defending the genome from the enemy within:mechanisms of retrotransposon suppression in the mouse germline
The viability of any species requires that the genome is kept stable as it is transmitted from generation to generation by the germ cells. One of the challenges to transgenerational genome stability is the potential mutagenic activity of transposable genetic elements, particularly retrotransposons. There are many different types of retrotransposon in mammalian genomes, and these target different points in germline development to amplify and integrate into new genomic locations. Germ cells, and their pluripotent developmental precursors, have evolved a variety of genome defence mechanisms that suppress retrotransposon activity and maintain genome stability across the generations. Here, we review recent advances in understanding how retrotransposon activity is suppressed in the mammalian germline, how genes involved in germline genome defence mechanisms are regulated, and the consequences of mutating these genome defence genes for the developing germline
IAP Display: A Simple Method to Identify Mouse Strain Specific IAP Insertions
Intracisternal A-type particle (IAP) elements are high copy number long terminal repeat (LTR) rodent retrotransposons. Some IAP elements can transpose, and are responsible for ~12% of spontaneous mouse mutations. Inbred mouse strains show variation in genomic IAP distribution, contributing to inter-strain genetic variability. Additionally IAP elements can influence the transcriptional regulation of neighbouring genes through their strong LTR promoter, effecting phenotypic variation. This genetic and phenotypic variability can translate into experimental variability between mouse strains. For example, it has been demonstrated that strain-specific genetic/epigenetic factors can interact to yield variable responses to drugs. Therefore, in experimental contexts it is essential to unequivocally identify mouse strains. Recently it was estimated that any two inbred strains share only ~40% of their IAP insertions. Of the remaining 60%, some insertions will be strain specific, fixed during inbreeding. These fixed insertions can be exploited as genetic markers to identify inbred strains, if they can be identified simply and efficiently. Here, we report the development of a PCR-based system allowing direct acquisition of strain-specific IAP insertions. In a pilot study, we identified 21 IAP loci, genotyped IAP insertions at 9 loci, and discovered two strain-specific insertions that could reliably identify these strains
Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations
We reconsider the conceptual foundations of the renormalization-group (RG)
formalism, and prove some rigorous theorems on the regularity properties and
possible pathologies of the RG map. Regarding regularity, we show that the RG
map, defined on a suitable space of interactions (= formal Hamiltonians), is
always single-valued and Lipschitz continuous on its domain of definition. This
rules out a recently proposed scenario for the RG description of first-order
phase transitions. On the pathological side, we make rigorous some arguments of
Griffiths, Pearce and Israel, and prove in several cases that the renormalized
measure is not a Gibbs measure for any reasonable interaction. This means that
the RG map is ill-defined, and that the conventional RG description of
first-order phase transitions is not universally valid. For decimation or
Kadanoff transformations applied to the Ising model in dimension ,
these pathologies occur in a full neighborhood of the low-temperature part of the first-order
phase-transition surface. For block-averaging transformations applied to the
Ising model in dimension , the pathologies occur at low temperatures
for arbitrary magnetic-field strength. Pathologies may also occur in the
critical region for Ising models in dimension . We discuss in detail
the distinction between Gibbsian and non-Gibbsian measures, and give a rather
complete catalogue of the known examples. Finally, we discuss the heuristic and
numerical evidence on RG pathologies in the light of our rigorous theorems.Comment: 273 pages including 14 figures, Postscript, See also
ftp.scri.fsu.edu:hep-lat/papers/9210/9210032.ps.
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