Calculabilit\'e de la cohomologie \'etale modulo l

Let $X$ be an algebraic scheme over an algebraically closed field and $\ell$ a prime number invertible on $X$. According to classical results (due essentially to A. Grothendieck, M. Artin and P. Deligne), the \'etale cohomology groups $\mathrm{H}^i(X,\mathbb{Z}/\ell\mathbb{Z})$ are finite-dimensional. Using an $\ell$-adic variant of M. Artin's good neighborhoods and elementary results on the cohomology of pro-$\ell$ groups, we express the cohomology of $X$ as a well controlled colimit of that of toposes constructed on $BG$ where the $G$ are computable finite $\ell$-groups. From this, we deduce that the Betti numbers modulo $\ell$ of $X$ are algorithmically computable (in the sense of Church-Turing). The proof of this fact, along with certain related results, occupies the first part of this paper. This relies on the tools collected in the second part, which deals with computational algebraic geometry. Finally, in the third part, we present a "universal" formalism for computation on the elements of a field.Comment: In French. v2 has been considerably reworked and expanded. v3 incorporates slight corrections and simplifications and a few additions (notably: computability of the morphism from hyper\v{c}ech cohomology, graded algebra structure, and a worked out example); submitted for publicatio

Composite Higgs Sketch

The coupling of a composite Higgs to the standard model fields can deviate substantially from the standard model values. In this case perturbative unitarity might break down before the scale of compositeness is reached, which would suggest that additional composites should lie well below this scale. In this paper we account for the presence of an additional spin 1 custodial triplet of rhos. We examine the implications of requiring perturbative unitarity up to the compositeness scale and find that one has to be close to saturating certain unitarity sum rules involving the Higgs and the rho couplings. Given these restrictions on the parameter space we investigate the main phenomenological consequences of the spin 1 triplet. We find that they can substantially enhance the Higgs di-photon rate at the LHC even with a reduced Higgs coupling to gauge bosons. The main existing LHC bounds arise from di-boson searches, especially in the experimentally clean channel where the charged rhos decay to a W-boson and a Z, which then decay leptonically. We find that a large range of interesting parameter space with 700 GeV < m(rho) < 2 TeV is currently experimentally viable.Comment: 37 pages, 12 figures; v4: sum rule corrected, conclusions unchange

Exploring T and S parameters in Vector Meson Dominance Models of Strong Electroweak Symmetry Breaking

We revisit the electroweak precision tests for Higgsless models of strong EWSB. We use the Vector Meson Dominance approach and express S and T via couplings characterizing vector and axial spin-1 resonances of the strong sector. These couplings are constrained by the elastic unitarity and by requiring a good UV behavior of various formfactors. We pay particular attention to the one-loop contribution of resonances to T (beyond the chiral log), and to how it can improve the fit. We also make contact with the recent studies of Conformal Technicolor. We explain why the second Weinberg sum rule never converges in these models, and formulate a condition necessary for preserving the custodial symmetry in the IR.Comment: 35 pages, 7 figures; v3: refs added, to appear in JHE

One-Loop Calculation of the Oblique S Parameter in Higgsless Electroweak Models

We present a one-loop calculation of the oblique S parameter within Higgsless models of electroweak symmetry breaking and analyze the phenomenological implications of the available electroweak precision data. We use the most general effective Lagrangian with at most two derivatives, implementing the chiral symmetry breaking SU(2)_L x SU(2)_R -> SU(2)_{L+R} with Goldstones, gauge bosons and one multiplet of vector and axial-vector massive resonance states. Using the dispersive representation of Peskin and Takeuchi and imposing the short-distance constraints dictated by the operator product expansion, we obtain S at the NLO in terms of a few resonance parameters. In asymptotically-free gauge theories, the final result only depends on the vector-resonance mass and requires M_V > 1.8 TeV (3.8 TeV) to satisfy the experimental limits at the 3 \sigma (1\sigma) level; the axial state is always heavier, we obtain M_A > 2.5 TeV (6.6 TeV) at 3\sigma (1\sigma). In strongly-coupled models, such as walking or conformal technicolour, where the second Weinberg sum rule does not apply, the vector and axial couplings are not determined by the short-distance constraints; but one can still derive a lower bound on S, provided the hierarchy M_V < M_A remains valid. Even in this less constrained situation, we find that in order to satisfy the experimental limits at 3\sigma one needs M_{V,A} > 1.8 TeV.Comment: 34 pages, 9 figures. Version published in JHEP. Some references and sentences have been added to facilitate the discussio

Six operations and Lefschetz-Verdier formula for Deligne-Mumford stacks

Laszlo and Olsson constructed Grothendieck's six operations for constructible complexes on Artin stacks in \'etale cohomology under an assumption of finite cohomological dimension, with base change established on the level of sheaves. In this article we give a more direct construction of the six operations for complexes on Deligne-Mumford stacks without the finiteness assumption and establish base change theorems in derived categories. One key tool in our construction is the theory of gluing finitely many pseudofunctors developed in arXiv:1211.1877. As an application, we prove a Lefschetz-Verdier formula for Deligne-Mumford stacks. We include both torsion and $\ell$-adic coefficients.Comment: 62 pages. v5, v4: minor improvements; v3: added a Lefschetz-Verdier formula; v2: moved the appendix in v1 to arXiv:1211.187

Seropositivity to Herpes Simplex Virus Antibodies and Risk of Alzheimer's Disease: A Population-Based Cohort Study

International audienceBACKGROUND: Herpes Simplex Virus (HSV) infection has been proposed as a possible risk factor of Alzheimer's Disease (AD) notably because it is neurotropic, ubiquitous in the general population and able to establish lifelong latency in the host. The fact that HSV was present in elderly subjects with AD suggests that the virus could be a co-factor of the disease. We investigated the risk of developing AD in anti-HSV immunoglobulin G (IgG) positive subjects (indicator of a lifelong infection to HSV) and IgM-positive subjects (indicator of primary infection or reactivation of the virus) in a longitudinal population-based cohort of elderly subjects living in the community. METHODS: Cox proportional hazard models were used to study the risk of developing AD according to the presence or not of anti-HSV IgG and IgM antibodies, assessed in the sera of 512 elderly initially free of dementia followed for 14 years. RESULTS: During the follow-up, 77 incident AD cases were diagnosed. Controlled for age, gender, educational level and Apolipoprotein E4 (APOE4) status, IgM-positive subjects showed a significant higher risk of developing AD (HR = 2.55; 95% CI [1.38-4.72]), although no significant increased risk was observed in IgG-positive subjects (HR = 1.67; 95%CI [0.75-3.73]). No modification effect with APOE4 status was found. CONCLUSION: Reactivation of HSV seropositivity is highly correlated with incident AD. HSV chronic infection may therefore be contributive to the progressive brain damage characteristic of AD

Oblique S and T Constraints on Electroweak Strongly-Coupled Models with a Light Higgs

Using a general effective Lagrangian implementing the chiral symmetry breaking SU(2)L x SU(2)R -> SU(2){L+R}, we present a one-loop calculation of the oblique S and T parameters within electroweak strongly-coupled models with a light scalar. Imposing a proper ultraviolet behaviour, we determine S and T at next-to-leading order in terms of a few resonance parameters. The constraints from the global fit to electroweak precision data force the massive vector and axial-vector states to be heavy, with masses above the TeV scale, and suggest that the W+W- and ZZ couplings of the Higgs-like scalar should be close to the Standard Model value. Our findings are generic, since they only rely on soft requirements on the short-distance properties of the underlying strongly-coupled theory, which are widely satisfied in more specific scenarios

Reducing AD-Like Pathology in 3xTg-AD Mouse Model by DNA Epitope Vaccine — A Novel Immunotherapeutic Strategy

BACKGROUND: The development of a safe and effective AD vaccine requires a delicate balance between providing an adequate anti-Abeta antibody response sufficient to provide therapeutic benefit, while eliminating an adverse T cell-mediated proinflammatory autoimmune response. To achieve this goal we have designed a prototype chemokine-based DNA epitope vaccine expressing a fusion protein that consists of 3 copies of the self-B cell epitope of Abeta(42) (Abeta(1-11)) , a non-self T helper cell epitope (PADRE), and macrophage-derived chemokine (MDC/CCL22) as a molecular adjuvant to promote a strong anti-inflammatory Th2 phenotype. METHODS AND FINDINGS: We generated pMDC-3Abeta(1-11)-PADRE construct and immunized 3xTg-AD mouse model starting at age of 3-4 months old. We demonstrated that prophylactic immunizations with the DNA epitope vaccine generated a robust Th2 immune response that induced high titers of anti-Abeta antibody, which in turn inhibited accumulation of Abeta pathology in the brains of older mice. Importantly, vaccination reduced glial activation and prevented the development of behavioral deficits in aged animals without increasing the incidence of microhemorrhages. CONCLUSIONS: Data from this transitional pre-clinical study suggest that our DNA epitope vaccine could be used as a safe and effective strategy for AD therapy. Future safety and immunology studies in large animals with the goal to achieve effective humoral immunity without adverse effects should help to translate this study to human clinical trials