On the non-commutative Iwasawa main conjecture for voltage covers of graphs

Let $p$ be a rational prime, and let $X$ be a connected finite graph. In this article we study voltage covers $X_\infty$ of $X$ attached to a voltage assignment ${\alpha}$ which takes values in some uniform $p$-adic Lie group $G$. We formulate and prove an Iwasawa main conjecture for the projective limit of the Picard groups $\text{Pic}(X_n)$ of the intermediate voltage covers $X_n$, ${n \in \mathbb{N}}$, and we prove one inclusion of a main conjecture for the projective limit of the Jacobians $J(X_n)$. Moreover, we study the $\mathfrak{M}_H(G)$-property of $\mathbb{Z}_p[[G]]$-modules and prove a necessary condition for this property which involves the $\mu$-invariants of $\mathbb{Z}_p$-subcovers ${Y \subseteq X_\infty}$ of $X$. If the dimension of $G$ is equal to 2, then this condition is also sufficient.Comment: 29 page

On the Gross order of vanishing conjecture for large vanishing orders

We prove the Gross order of vanishing conjecture in special cases where the vanishing order of the character in question can be arbitrarily large. In almost all previously known cases the vanishing order is zero or one. One major ingredient of our proofs is the equivalence of this conjecture to the Gross-Kuz'min conjecture. We present here a direct proof of this equivalence, using only the known validity of the Iwasawa Main Conjecture over totally real fields

Genotypic and phenotypic variation among Staphylococcus saprophyticus from human and animal isolates

<p>Abstract</p> <p>Background</p> <p>The main aim of this study was to examine the genotypic and phenotypic diversity of <it>Staphylococcus saprophyticus </it>isolates from human and animal origin.</p> <p>Findings</p> <p>In total, 236 clinical isolates and 15 animal isolates of <it>S. saprophyticus </it>were characterized in respect of the occurrence of 9 potential virulence genes and four surface properties. All strains were PCR positive for the regulatory genes <it>agr</it>, <it>sar</it>>it>A and <it>rot </it>as well as for the surface proteins UafA and Aas. Nearly 90% of the clinical isolates were found to possess the gene for the surface-associated lipase Ssp and 10% for the collagen binding MSCRAMM SdrI. All animal isolates were negative for<it>sdrI</it>. Lipolytic activity could be detected in 66% of the clinical and 46% of the animal isolates. Adherence to collagen type I was shown of 20% of the clinical strains and 6% of the strains of animal origin. Most <it>S. saprophyticus </it>strains showed hydrophobic properties and only few could agglutinate sheep erythrocytes.</p> <p>Conclusions</p> <p>We described a broad analysis of animal and human <it>S. saprophyticus </it>isolates regarding virulence genes and phenotypic properties such as lipase activity, hydrophobicity, and adherence. While <it>S. saprophyticus </it>strains from animal sources have prerequisites for colonization of the urinary tract like the D-serine-deaminase, out findings suggested that they need to acquire new genes e.g. MSCRAMMS for adherence like sdrI and to modulate their existing properties e.g. increasing the lipase activity or reducing hydrophobicity. These apparently important new genes or properties for virulence have to be further analyzed.</p

Fine Selmer groups of modular forms

We compare the Iwasawa invariants of fine Selmer groups of $p$-adic Galois representations over admissible $p$-adic Lie extensions of a number field $K$ to the Iwasawa invariants of ideal class groups along these Lie extensions. More precisely, let $K$ be a number field, let $V$ be a $p$-adic representation of the absolute Galois group $G_K$ of $K$, and choose a $G_K$-invariant lattice ${T \subseteq V}$. We study the fine Selmer groups of ${A = V/T}$ over suitable $p$-adic Lie extensions $K_\infty/K$, comparing their corank and $\mu$-invariant to the corank and the $\mu$-invariant of the Iwasawa module of ideal class groups in $K_\infty/K$. In the second part of the article, we compare the Iwasawa $\mu$- and $l_0$-invariants of the fine Selmer groups of CM modular forms on the one hand and the Iwasawa invariants of ideal class groups on the other hand over trivialising multiple $\mathbb{Z}_p$-extensions of $K$