Generalised Kawada-Satake method for Mackey functors in class field theory

We propose and study a generalised Kawada--Satake method for Mackey functors in the class field theory of positive characteristic. The root of this method is in the use of explicit pairings, such as the Artin--Schreier--Witt pairing, for groups describing abelian extensions. We separate and simplify the algebraic component of the method and discuss a relation between the existence theorem in class field theory and topological reflexivity with respect to the explicit pairing. We apply this method to derive higher local class field theory of positive characteristic, using advanced properties of topological Milnor K-groups of such fields

De novo sequencing and characterization of floral transcriptome in two species of buckwheat (Fagopyrum)

<p>Abstract</p> <p>Background</p> <p>Transcriptome sequencing data has become an integral component of modern genetics, genomics and evolutionary biology. However, despite advances in the technologies of DNA sequencing, such data are lacking for many groups of living organisms, in particular, many plant taxa. We present here the results of transcriptome sequencing for two closely related plant species. These species, <it>Fagopyrum esculentum </it>and <it>F. tataricum</it>, belong to the order Caryophyllales - a large group of flowering plants with uncertain evolutionary relationships. <it>F. esculentum </it>(common buckwheat) is also an important food crop. Despite these practical and evolutionary considerations <it>Fagopyrum </it>species have not been the subject of large-scale sequencing projects.</p> <p>Results</p> <p>Normalized cDNA corresponding to genes expressed in flowers and inflorescences of <it>F. esculentum </it>and <it>F. tataricum </it>was sequenced using the 454 pyrosequencing technology. This resulted in 267 (for <it>F. esculentum</it>) and 229 (<it>F. tataricum</it>) thousands of reads with average length of 341-349 nucleotides. <it>De novo </it>assembly of the reads produced about 25 thousands of contigs for each species, with 7.5-8.2× coverage. Comparative analysis of two transcriptomes demonstrated their overall similarity but also revealed genes that are presumably differentially expressed. Among them are retrotransposon genes and genes involved in sugar biosynthesis and metabolism. Thirteen single-copy genes were used for phylogenetic analysis; the resulting trees are largely consistent with those inferred from multigenic plastid datasets. The sister relationships of the Caryophyllales and asterids now gained high support from nuclear gene sequences.</p> <p>Conclusions</p> <p>454 transcriptome sequencing and <it>de novo </it>assembly was performed for two congeneric flowering plant species, <it>F. esculentum </it>and <it>F. tataricum</it>. As a result, a large set of cDNA sequences that represent orthologs of known plant genes as well as potential new genes was generated.</p