Lifting vector bundles to Witt vector bundles

Let $p$ be a prime, and let $S$ be a scheme of characteristic $p$. Let $n \geq 2$ be an integer. Denote by $\mathbf{W}_n(S)$ the scheme of Witt vectors of length $n$, built out of $S$. The main objective of this paper concerns the question of extending (=lifting) vector bundles on $S$ to vector bundles on $\mathbf{W}_n(S)$. After introducing the formalism of Witt-Frobenius Modules and Witt vector bundles, we study two significant particular cases, for which the answer is positive: that of line bundles, and that of the tautological vector bundle of a projective space. We give several applications of our point of view to classical questions in deformation theory---see the Introduction for details. In particular, we show that the tautological vector bundle of the Grassmannian $Gr_{\mathbb{F}_p}(m,n)$ does not extend to $\mathbf{W}_2(Gr_{\mathbb{F}_p}(m,n))$, if $2 \leq m \leq n-2$. In the Appendix, we give algebraic details on our (new) approach to Witt vectors, using polynomial laws and divided powers. It is, we believe, very convenient to tackle lifting questions.Comment: Enriched version, with an appendi

Conference Conversations: Monique Charles on Corbyn and Grime

Yesterday Renewal co-hosted an event with The Corbyn Effect at Momentum’s conference, The World Transformed, in Brighton. One of the speakers, Monique Charles, recently completed a PhD on grime music. In The Corbyn Effect she looks at the phenomenon of Grime for Corbyn, and we had coffee with her to talk about her work, Jeremy Corbyn, and the Labour Party

Smooth profinite groups, III: the Smoothness Theorem

Let $p$ be a prime. The goal of this article is to prove the Smoothness Theorem 5.1 (Theorem D), which notably asserts that a $(1,\infty)$-cyclotomic pair is $(n,1)$-cyclotomic, for all $n \geq 1$. In the particular case of Galois cohomology, the Smoothness Theorem provides a new proof of the Norm Residue Isomorphism Theorem. Using the formalism of smooth profinite groups, this proof presents it as a consequence of Kummer theory for fields.Comment: Added index for reader's convenience. Comments welcom

LIFE CYCLE ASSESSMENT OF A HEMP CONCRETE WALL: IMPACT OF THICKNESS AND COATING.

International audienceIn a context of sustainable development and energy sparing, a life cycle assessment (LCA) may be useful to make good choices. Thus, this study concerns the LCA of an environmentally friendly material used for building construction, hemp concrete. The functional unit is first defined per square such that the wall may provide the function of bearing wall meter and its thermal performance is described by a thermal resistance of 2.78 m².K/W. The results then showed that the production phase of raw materials is mainly responsible for the environmental impact of the wall, mostly due to the binder production. It was also shown that, compared to traditional construction materials, hemp concrete has a low impact on environment. Moreover, hemp concrete contributes to reduce climate change as photosynthesis-mediated carbon sequestration and carbonation serve to reduce atmospheric carbon dioxide. A sensitivity analysis is performed on three criteria: wall thickness, renewal of coatings and compounds of the indoor coating. Our results show that environmental indicators evolve with wall thickness, except for the climate change indicator. It improves with thickness due to carbon sequestration and carbonation. Moreover the increase in the wall's thermal resistance with wall thickness is not taken into account in such an LCA performed at the material level. The renewal of coating slightly impacts the environmental indicator for small numbers of renewals but it leads to negative effects if they are too numerous. It appears that hemp-lime coating has a greater impact than sand-lime coating as it embeds more binder

Secondary Plant Metabolites as Potent Drug Candidates against antimicrobial-Resistant Pathogens

Antibiotic resistance is a major public health threat of the twenty-first century and represents an important risk to the global economy. Healthcare-associated infections mainly caused by drug-resistant bacteria are wreaking havoc in patient care worldwide. The spread of such pathogens limits the utility of available drugs and complicates the treatment of bacterial diseases. As a result, there is an urgent need for new drugs with mechanisms of action capable of curbing resistance. Plants synthesize and utilize various metabolic compounds to deter pathogens and predators. Utilizing these plant-based metabolites is a promising option in identifying novel bioactive compounds that could be harnessed to develop new potent antimicrobial drugs to treat multidrug-resistant pathogens. The purpose of this review is to highlight medicinal plants as important sources of novel antimicrobial agents that could be developed to help combat antimicrobial resistance

Carbamazepine on a carbamazepine monolayer forms unique 1D supramolecular assemblies

High-resolution STM imaging of the structures formed by carbamazepine molecules adsorbed onto a pseudo-ordered carbamazepine monolayer on Au(111) shows the formation of previously unreported 1-dimensional supramolecular assemblies

Template Matching with Noisy Patches: A Contrast-Invariant GLR Test

International audienceMatching patches from a noisy image to atoms in a dictionary of patches is a key ingredient to many techniques in image processing and computer vision. By representing with a single atom all patches that are identical up to a radiometric transformation, dictionary size can be kept small, thereby retaining good computational efficiency. Identification of the atom in best match with a given noisy patch then requires a contrast-invariant criterion. In the light of detection theory, we propose a new criterion that ensures contrast invariance and robustness to noise. We discuss its theoretical grounding and assess its performance under Gaussian, gamma and Poisson noises