Universal deformation rings of modules over Frobenius algebras

Let $k$ be a field, and let $\Lambda$ be a finite dimensional $k$-algebra. We prove that if $\Lambda$ is a self-injective algebra, then every finitely generated $\Lambda$-module $V$ whose stable endomorphism ring is isomorphic to $k$ has a universal deformation ring $R(\Lambda,V)$ which is a complete local commutative Noetherian $k$-algebra with residue field $k$. If $\Lambda$ is also a Frobenius algebra, we show that $R(\Lambda,V)$ is stable under taking syzygies. We investigate a particular Frobenius algebra $\Lambda_0$ of dihedral type, as introduced by Erdmann, and we determine $R(\Lambda_0,V)$ for every finitely generated $\Lambda_0$-module $V$ whose stable endomorphism ring is isomorphic to $k$.Comment: 25 pages, 2 figures. Some typos have been fixed, the outline of the paper has been changed to improve readabilit

Tannakian duality for Anderson-Drinfeld motives and algebraic independence of Carlitz logarithms

We develop a theory of Tannakian Galois groups for t-motives and relate this to the theory of Frobenius semilinear difference equations. We show that the transcendence degree of the period matrix associated to a given t-motive is equal to the dimension of its Galois group. Using this result we prove that Carlitz logarithms of algebraic functions that are linearly independent over the rational function field are algebraically independent.Comment: 39 page

Exorcising Grice’s ghost : an empirical approach to studying intentional communication in animals

Language’s intentional nature has been highlighted as a crucial feature distinguishing it from other communication systems. Specifically, language is often thought to depend on highly structured intentional action and mutual mindreading by a communicator and recipient. Whilst similar abilities in animals can shed light on the evolution of intentionality, they remain challenging to detect unambiguously. We revisit animal intentional communication and suggest that progress in identifying analogous capacities has been complicated by (i) the assumption that intentional (that is, voluntary) production of communicative acts requires mental-state attribution, and (ii) variation in approaches investigating communication across sensory modalities. To move forward, we argue that a framework fusing research across modalities and species is required. We structure intentional communication into a series of requirements, each of which can be operationalised, investigated empirically, and must be met for purposive, intentionally communicative acts to be demonstrated. Our unified approach helps elucidate the distribution of animal intentional communication and subsequently serves to clarify what is meant by attributions of intentional communication in animals and humans

Topics on modular Galois representations modulo prime powers

This article surveys modularity, level raising and level lowering questions for two-dimensional representations modulo prime powers of the absolute Galois group of the rational numbers. It contributes some new results and describes algorithms and a database of modular forms orbits and higher congruences

Updated S2 K guidelines for the management of bullous pemphigoid initiated by the European Academy of Dermatology and Venereology (EADV).

BACKGROUND Bullous pemphigoid (BP) is the most common autoimmune subepidermal blistering disease of the skin and mucous membranes. This disease typically affects the elderly and presents with itch and localized or, most frequently, generalized bullous lesions. A subset of patients only develops excoriations, prurigo-like lesions, and eczematous and/or urticarial erythematous lesions. The disease, which is significantly associated with neurological disorders, has high morbidity and severely impacts the quality of life. OBJECTIVES AND METHODOLOGY The Autoimmune blistering diseases Task Force of the European Academy of Dermatology and Venereology sought to update the guidelines for the management of BP based on new clinical information, and new evidence on diagnostic tools and interventions. The recommendations are either evidence-based or rely on expert opinion. The degree of consent among all task force members was included. RESULTS Treatment depends on the severity of BP and patients' comorbidities. High-potency topical corticosteroids are recommended as the mainstay of treatment whenever possible. Oral prednisone at a dose of 0.5 mg/kg/day is a recommended alternative. In case of contraindications or resistance to corticosteroids, immunosuppressive therapies, such as methotrexate, azathioprine, mycophenolate mofetil or mycophenolate acid, may be recommended. The use of doxycycline and dapsone is controversial. They may be recommended, in particular, in patients with contraindications to oral corticosteroids. B-cell-depleting therapy and intravenous immunoglobulins may be considered in treatment-resistant cases. Omalizumab and dupilumab have recently shown promising results. The final version of the guideline was consented to by several patient organizations. CONCLUSIONS The guidelines for the management of BP were updated. They summarize evidence- and expert-based recommendations useful in clinical practice

Plasticity of Blood- and Lymphatic Endothelial Cells and Marker Identification

Peer reviewe