Stickelberger series and Main Conjecture for function fields

Let F be a global function field of characteristic p with ring of integers A and let Φ be a Hayes module on the Hilbert class field H_A of F. We prove an Iwasawa Main Conjecture for the (Z_p)^∞-extension mathcal{F}/F generated by the mathfrak{p}-power torsion of Φ (mathfrak{p} a prime of A). The main tool is a Stickelberger series whose specialization provides a generator for the Fitting ideal of the class group of F. Moreover we prove that the same series, evaluated at complex or mathfrak{p}-adic characters, interpolates the Goss Zeta-function or some mathfrak{p}-adic L-function, thus providing the link between the algebraic structure (class groups) and the analytic functions, which is the crucial part of Iwasawa Main Conjecture

Stickelberger series and Main Conjecture for function fields

Let F be a global function field of characteristic p with ring of integers A and let \Phi be a Hayes module on the Hilbert class field H(A) of F. We prove an Iwasawa Main Conjecture for the Z_p^\infty-extension F/F generated by the \mathfrak{p}-power torsion of \Phi (\mathfrak{p} a prime of A). The main tool is a Stickelberger series whose specialization provides a generator for the Fitting ideal of the class group of F. Moreover we prove that the same series, evaluated at complex or p-adic characters, interpolates the Goss Zeta-function or some p-adic L-function, thus providing the link between the algebraic structure (class groups) and the analytic functions, which is the crucial part of Iwasawa Main Conjecture.Comment: to appear in Publicacions Matem\`atique

STICKELBERGER SERIES AND IWASAWA MAIN CONJECTURE FOR FUNCTION FIELDS

Let F be a global function \ufb01eld in characteristic p>0. There exists many di\ufb00erent types of L-functions that can be associated to F, such as the Artin L-functions, the Goss Zeta function or the p-adic L-functions. In this work i have investigated the correlations between these analytic objects and the Stickelberger series, which is a formal power series whose coe\ufb03cients lie in a suitable Galois algebra. In the second part of this work i have studied the Iwasawa extension generated by the p-torsion of a Hayes module and i have used the Stickelberger series to prove a "main conjecture" for the p-part of the class group

Dispersion engineering of highly nonlinear chalcogenide suspended-core fibers

Chalcogenide optical fibers are currently undergoing intensive investigation with the aim of exploiting the excellent glass transmission and nonlinear characteristics in the near- and mid-infrared for several applications. Further enhancement of these properties can be obtained, for a particular application, with optical fibers specifically designed that are capable of providing low effective area together with a properly tailored dispersion, matching the characteristics of the laser sources used to excite nonlinear effects. Suspended-core photonic crystal fibers are ideal candidates for nonlinear applications, providing small-core waveguides with large index contrast and tunable dispersion. In this paper, the dispersion properties of As2S3 suspended-core fibers are numerically analyzed, taking into account, for the first time, all the structural parameters, including the size and the number of the glass bridges. The results show that a proper design of the cladding struts can be exploited to significantly change the fiber properties, altering the maximum value of the dispersion parameter and shifting the zero-dispersion wavelengths over a range of 400 nm

Chalcogenide suspended-core fibers for supercontinuum generation in the mid-infrared

Chalcogenide suspended core fibers are a valuable solution to obtain supercontinuum generation of light in the mid-infrared, thanks to glass high transparency, high index contrast, small core diameter and widely-tunable dispersion. In this work the dispersion and nonlinear properties of several chalcogenide suspended core mi-crostructured fibers are numerically evaluated, and the effects of all the structural parameters are investigated. Optimization of the design is carried out to provide a fiber suitable for wide-band supercontinuum generation in the mid-infrared

Highly nonlinear chalcogenide suspended-core fibers for applications in the mid-infrared

Due to their unique dispersion and nonlinear properties, chalcogenide suspended-core fibers, characterized by a few micrometer-sized core suspended between large air-holes by few small glaß struts, are excellent candidates for mid-infrared applications. In the present study the influence of the main croß-section characteristics of the chalcogenide suspended-core fibers on the dispersion curve and on the position of the zero-dispersion wavelength has been thoroughly analyzed with a full-vector modal solver based on the finite element. In particular, the design of suspended-core fibers made of both As2S3 and As2Se3 has been optimized to obtain dispersion properties suitable for the supercontinuum generation in the mid-infrared

Estudio de la patogenia y de los mecanismos inmunológicos en la infección por Aeromonas salmonicida subsp. salmonicida en rodaballo (Scophthalmus maximus)

A. salmonicida subsp. salmonicida (A. salmonicida) es uno de los principales patógenos de los peces, incluido el rodaballo. En esta memoria hemos profundizado en el conocimiento de la enfermedad causada por A. salmonicida y el efecto la vacunación en el rodaballo, abordando aspectos relacionados con las lesiones, el diagnóstico, la patogenia y la respuesta inmunitaria. La identificación del antígeno bacteriano se llevó a cabo mediante el desarrollo de una técnica inmunohistoquímica, la cual demostró ser una herramienta útil para el estudio y el diagnóstico de la enfermedad. La forma aguda de la enfermedad se analizó a partir de un modelo experimental de infección. Los peces desafiados desarrollaron septicemia, observándose el antígeno bacteriano de forma libre dentro de vasos sanguíneos y en tejidos. Además, el antígeno bacteriano se localizó dentro de fagocitos mononucleares, indicando su endocitosis y la posible supervivencia intracelular del patógeno. Los peces infectados mostraron un incremento significativo del número de células inmunorreactivas para el TNF-α y la enzima iNOS en los órganos linfo-hematopoyéticos, sugiriendo la activación de los fagocitos y su participación en la respuesta inmunitaria. A su vez, el incremento de la actividad de estos efectores inmunitarios durante un proceso septicémico podría estar implicado en la patogenia de la enfermedad. La forma crónica de la enfermedad se describió a partir de rodaballos de cultivo. Esta forma de enfermedad se caracterizó por el desarrollo de granulomas dérmicos, lo cual señala la importancia de la inmunidad celular frente a la infección. Las reacciones granulomatosas también denotan un posible fallo en la eliminación del patógeno, por lo que estos hallazgos aportan datos relevantes a fin de identificar peces enfermos que podrían actuar como fuente de infección. Finalmente, se evaluó la eficacia de vacunas (acuosa y oleosa) formuladas con bacterinas. Mediante un ensayo experimental se analizó el grado de protección, las lesiones ocasionadas por la vacunación y la cinética del antígeno vacunal. La vacuna oleosa mostró una protección moderada a los 90 días post-vacunación. El adyuvante oleoso generó una celomitis granulomatosa, detectándose el antígeno vacunal asociado al material oleoso. La vacuna acuosa causó una celomitis leve y el antígeno vacunal se localizó en fagocitos mononucleares dentro de cavidad celómica, riñón y bazo. No obstante, la vacuna acuosa no indujo protección. En este trabajo se demostró que el análisis histológico e inmunohistoquímico resultan imprescindibles para evaluar el efecto y la inocuidad de las vacunas frente a A. salmonicida, con el propósito de contribuir a determinar la eficacia de las mismas en el rodaballo

Stickelberger series and Main Conjecture for function fields

Let F be a global function field of characteristic p with ring of integers A and let Φ be a Hayes module on the Hilbert class field HA of F. We prove an Iwasawa Main Conjecture for the Z∞p extension F/F generated by the p-power torsion of Φ (p a prime of A). The main tool is a Stickelberger series whose specialization provides a generator for the Fitting ideal of the class group of F. Moreover we prove that the same series, evaluated at complex or p-adic characters, interpolates the Goss Zeta-function or some p-adic L-function, thus providing the link between the algebraic structure (class groups) and the analytic functions, which is the crucial part of Iwasawa Main Conjecture