1,720,974 research outputs found
Analytic subvarieties with many rational points
No full textWe give a generalization of the classical Bombieri–Schneider–Lang criterion in transcendence theory. We give a local notion of LG-germ, which is similar to the notion of E-function and Gevrey condition, and which generalize (and replace) the condition on derivatives in the theorem quoted above. Let KC be a number field and X a quasi-projective variety defined over K. Let γ : M → X be an holomorphic map of finite order from a parabolic Riemann surface to X such that the Zariski closure of the image of it is strictly bigger then one. Suppose that for every pX(K)(M) the formal germ of M near P is an LG-germ, then we prove that X(K)(M) is a finite set. Then we define the notion of conformally parabolic Kähler varieties; this generalize the notion of parabolic Riemann surface. We show that on these varieties we can define a value distribution theory. The complementary of a divisor on a compact Kähler manifold is conformally parabolic; in particular every quasi projective variety is. Suppose that A is conformally parabolic variety of dimension m over C with Kähler form ω and γ : A → X is an holomorphic map of finite order such that the Zariski closure of the image is strictly bigger then m. Suppose that for every pX(K)(A) , the image of A is an LG-germ. then we prove that there exists a current T on A of bidegree (1, 1) such that ATm−1 explicitly bounded and with Lelong number bigger or equal then one on each point in γ −1(X(K)). In particular if A is affine γ −1(X(K)) is not Zariski dense
Dyson's theorem for curves
No full textLet K be a number field and X-1 and X-2 two smooth projective curves defined over it. In this paper we prove an analogue of the Dyson theorem for the product X-1 x X-2. If X-i = P-1 we find the classical Dyson theorem. In general, it will imply a self contained and easy proof of Siegel theorem oil integral points oil hyperbolic curves and it will give some insight on effectiveness. This proof is new and avoids the use of Roth and Mordell-Weil theorems, the theory of Linear Forms in Logarithms and the Schmidt subspace theorem. (C) 2008 Elsevier Inc. All rights reserved
Horizontal sections of connections on curves and transcendence
No full textLet K be a number field, X be a smooth projective curve over it and D be a reduced divisor on X. Let (E,∇) be a fibre bundle with connection having
meromorphic poles on D. Let p1,...,ps ∈ X(K) and X := X \ {D,p1,...,ps} (the pj’s may be in the support of D). Using tools from Nevanlinna theory and formal geometry, we give the definition of E–section of type α of the vector bundle E with respect to the points pj ; this is the natural generalization of the notion of E function defined in Siegel Shidlowski theory. We prove that the value of a E–section of type α in an algebraic point different from the pj’s has maximal transcendence degree. Siegel Shidlowski theorem is a special case of the theorem proved. We give an application to isomonodromic connections
The strong abc conjecture over function fields [after McQuillan and Yamanoi]
Full text linkThe conjecture predicts a highly non trivial upper bound for
the height of an algebraic point in terms of its discriminant and
its intersection with a fixed divisor of the projective line counted
without multiplicity. We will report on the two independent proofs
of the strong conjecture over function fields given by
McQuillan and Yamanoi. The first proof relies on tools from
differential and algebraic geometry; the second relies on analytic
and topological methods. They correspond respectively to the
Nevanlinna and the Ahlfors approach to the Nevanlinna Second Main
Theorem
Roth's theorem for ruled surfaces
No full textThis paper addresses conjectures of E. Bombieri and P. Vojta in the special case of ruled surfaces not birational to 2. Apart from this implicit restriction to 1 bundles S over an elliptic curve, the ultimate question of the arithmetic of pairs (S,D) for a divisor D requires further restrictions on D which turn the proposed conjectures into the study of Roth's theorem on approximation of algebraic numbers α, but for α now parametrized by an elliptic curve. With these restrictions, best possible answers are obtained. The same study may also be carried out for holomorphic maps, and this is done simultaneousl
Torsors under some group schemes of order pn
No full textLet R be a complete dvr with perfect residue field k of characteristic p > 0. Let {G(lambda))lambda is an element of R be the class of R-affine, commutative, smooth of relative dimension one group schemes generically isomorphic to G(m). Let G := {G(lambda,n))(lambda is an element of R,n is an element of N) be the class of finite flat commutative group schemes of order p(n) defined as kernels of the isogenies phi(lambda,n):G(lambda)-> G((lambda pn)). We provide an explicit description of torsors over R-schemes under the group schemes G(lambda) and G(lambda,n). (C) 2007 Elsevier Inc. All rights reserved
The canonical subgroup for families of abelian varieties
Get PDFLet V be a complete discrete valuation ring with residue field k of characteristic p > 0 and fraction field K of characteristic zero. Let S be a formal scheme over V and let X -> S be a locally projective formal abelian scheme. In this paper we prove that, under suitable natural conditions on the Hasse-Witt matrix of X circle times(V) V/pV, the kernel of the Frobenius morphism on X-k can be canonically lifted to a finite and flat subgroup scheme of X over an admissible blow-up of S, called the 'canonical subgroup of X'. This is done by a careful study of torsors under group schemes of order p over X. We also present a filtration on H-1 (3C, mu(p)) in the spirit of the Hodge-Tate decomposition
Prediction and modeling of protein–protein interactions using “Spotted” peptides with a template-based approach
Full text linkProtein–peptide interactions (PpIs) are a subset of the overall protein–protein interaction (PPI) network in the living cell and are pivotal for the majority of cell processes and functions. High-throughput methods to detect PpIs and PPIs usually require time and costs that are not always affordable. Therefore, reliable in silico predictions represent a valid and effective alternative. In this work, a new algorithm is described, implemented in a freely available tool, i.e., “PepThreader”, to carry out PPIs and PpIs prediction and analysis. PepThreader threads multiple fragments derived from a full-length protein sequence (or from a peptide library) onto a second template peptide, in complex with a protein target, “spotting” the potential binding peptides and ranking them according to a sequence-based and structure-based threading score. The threading algorithm first makes use of a scoring function that is based on peptides sequence similarity. Then, a rerank of the initial hits is performed, according to structure-based scoring functions. PepThreader has been benchmarked on a dataset of 292 protein–peptide complexes that were collected from existing databases of experimentally determined protein–peptide interactions. An accuracy of 80%, when considering the top predicted 25 hits, was achieved, which performs in a comparable way with the other state-of-art tools in PPIs and PpIs modeling. Nonetheless, PepThreader is unique in that it is able at the same time to spot a binding peptide within a full-length sequence involved in PPI and model its structure within the receptor. Therefore, PepThreader adds to the already-available tools supporting the experimental PPIs and PpIs identification and characterization
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