Completed cohomology of Shimura curves and a p-adic Jacquet-Langlands correspondence

We study indefinite quaternion algebras over totally real fields F, and give an example of a cohomological construction of p-adic Jacquet-Langlands functoriality using completed cohomology. We also study the (tame) levels of p-adic automorphic forms on these quaternion algebras and give an analogue of Mazur's `level lowering' principle.Comment: Updated version. Contains some minor corrections compared to the published versio

Collapsible Pushdown Parity Games

International audienceThis paper studies a large class of two-player perfect-information turn-based parity games on infinite graphs, namely those generated by collapsible pushdown automata. The main motivation for studying these games comes from the connections from collapsible pushdown automata and higher-order recursion schemes, both models being equi-expressive for generating infinite trees. Our main result is to establish the decidability of such games and to provide an effective representation of the winning region as well as of a winning strategy. Thus, the results obtained here provide all necessary tools for an in-depth study of logical properties of trees generated by collapsible pushdown automata/recursion schemes

On elliptic factors in real endoscopic transfer I

This paper is concerned with the structure of packets of representations and some refinements that are helpful in endoscopic transfer for real groups. It includes results on the structure and transfer of packets of limits of discrete series representations. It also reinterprets the Adams-Johnson transfer of certain nontempered representations via spectral analogues of the Langlands-Shelstad factors, thereby providing structure and transfer compatible with the associated transfer of orbital integrals. The results come from two simple tools introduced here. The first concerns a family of splittings of the algebraic group G under consideration; such a splitting is based on a fundamental maximal torus of G rather than a maximally split maximal torus. The second concerns a family of Levi groups attached to the dual data of a Langlands or an Arthur parameter for the group G. The introduced splittings provide explicit realizations of these Levi groups. The tools also apply to maps on stable conjugacy classes associated with the transfer of orbital integrals. In particular, they allow for a simpler version of the definitions of Kottwitz-Shelstad for twisted endoscopic transfer in certain critical cases. The paper prepares for spectral factors in twisted endoscopic transfer that are compatible in a certain sense with the standard factors discussed here. This compatibility is needed for Arthur's global theory. The twisted factors themselves will be defined in a separate paper.Comment: 48 pages, to appear in Progress in Mathematics, Volume 312, Birkha\"user. Also renumbering to match that of submitted versio

Elliptic Curves over Real Quadratic Fields are Modular

We prove that all elliptic curves defined over real quadratic fields are modular.Comment: 38 pages. Magma scripts available as ancillary files with this arXiv versio

Symbolic Backwards-Reachability Analysis for Higher-Order Pushdown Systems

Higher-order pushdown systems (PDSs) generalise pushdown systems through the use of higher-order stacks, that is, a nested "stack of stacks" structure. These systems may be used to model higher-order programs and are closely related to the Caucal hierarchy of infinite graphs and safe higher-order recursion schemes. We consider the backwards-reachability problem over higher-order Alternating PDSs (APDSs), a generalisation of higher-order PDSs. This builds on and extends previous work on pushdown systems and context-free higher-order processes in a non-trivial manner. In particular, we show that the set of configurations from which a regular set of higher-order APDS configurations is reachable is regular and computable in n-EXPTIME. In fact, the problem is n-EXPTIME-complete. We show that this work has several applications in the verification of higher-order PDSs, such as linear-time model-checking, alternation-free mu-calculus model-checking and the computation of winning regions of reachability games

The supercuspidal representations of p-adic classical groups

Let G be a unitary, symplectic or special orthogonal group over a locally compact non-archimedean local field of odd residual characteristic. We construct many new supercuspidal representations of G, and Bushnell-Kutzko types for these representations. Moreover, we prove that every irreducible supercuspidal representation of G arises from our constructions.Comment: 55 pages -- minor changes from 1st version (mostly in sections 2.2, 4.2 and 6.2). To appear in Inventiones mathematicae, 2008 (DOI is not yet active as at 12 Nov 2007

Protein quantitative trait locus study in obesity during weight-loss identifies a leptin regulator

Although many genetic variants are known for obesity, their function remains largely unknown. Here, in a weight-loss intervention cohort, the authors identify protein quantitative trait loci associated with BMI at baseline and after weight loss and find FAM46A to be a regulator of leptin in adipocytes

On a Conjecture of Rapoport and Zink

In their book Rapoport and Zink constructed rigid analytic period spaces $F^{wa}$ for Fontaine's filtered isocrystals, and period morphisms from PEL moduli spaces of $p$-divisible groups to some of these period spaces. They conjectured the existence of an \'etale bijective morphism $F^a \to F^{wa}$ of rigid analytic spaces and of a universal local system of $Q_p$-vector spaces on $F^a$. For Hodge-Tate weights $n-1$ and $n$ we construct in this article an intrinsic Berkovich open subspace $F^0$ of $F^{wa}$ and the universal local system on $F^0$. We conjecture that the rigid-analytic space associated with $F^0$ is the maximal possible $F^a$, and that $F^0$ is connected. We give evidence for these conjectures and we show that for those period spaces possessing PEL period morphisms, $F^0$ equals the image of the period morphism. Then our local system is the rational Tate module of the universal $p$-divisible group and enjoys additional functoriality properties. We show that only in exceptional cases $F^0$ equals all of $F^{wa}$ and when the Shimura group is $GL_n$ we determine all these cases.Comment: v2: 48 pages; many new results added, v3: final version that will appear in Inventiones Mathematica

Penetrance of HNPCC-related cancers in a retrolective cohort of 12 large Newfoundland families carrying a MSH2 founder mutation: an evaluation using modified segregation models

<p>Abstract</p> <p>Background</p> <p>Accurate risk (penetrance) estimates for associated phenotypes in carriers of a major disease gene are important for genetic counselling of at-risk individuals. Population-specific estimates of penetrance are often needed as well. Families ascertained from high-risk disease clinics provide substantial data to estimate penetrance of a disease gene, but these estimates must be adjusted for possible specific sources of bias.</p> <p>Methods</p> <p>A cohort of 12 independently ascertained HNPCC families harbouring a founder MSH2 mutation was identified from a cancer genetics clinic in St. John's, Newfoundland, Canada. Carrier status was known for 247 family members but phenotype information on up to 85 additional relatives with unknown carrier status was available; using modified segregation models these additional individuals could be included in the analyses. Three HNPCC-related phenotypes were evaluated as age at diagnosis of: any HNPCC cancer (first cancer), colorectal cancer (CRC), and endometrial cancer (EC) for females.</p> <p>Results</p> <p>Lifetime (age 70) risk estimates for male and female carriers were similar for developing any HNPCC cancer (Males = 98.2%, 95% Confidence Interval (CI) = (93.8%, 99.9%); Females = 92.8%, 95% CI = (82.4%, 99.1%)) but female carriers experienced substantially reduced lifetime risk for developing CRC compared to male carriers (Females = 38.9%, 95% CI = (24.2%, 62.1%); Males = 84.5%, 95% CI = (67.3%, 91.3%)). Female non-carriers had very low lifetime risk for these two outcomes while male non-carriers had lifetime risks intermediate to the female carriers and non-carriers. Female carriers had a lifetime risk of developing EC of 82.4%. Relative risks for developing any HNPCC cancer (carriers relative to non-carriers) were substantially greater for females compared to their male counterparts (Females = 54.8, 95%CI = (4.4, 379.8); Males = 9.7, 95% CI = (0.3, 23.8)). Relative risks for developing CRC at age 70 were substantially greater for females compared to their male counterparts (Females = 23.7, 95%CI = (5.6, 137.9); Males = 6.8%, 95% CI = (2.3, 66.2)). However, the risk of developing CRC decreased with age among both genders.</p> <p>Conclusion</p> <p>The proposed modified segregation-based models used to estimate age-specific risks for HNPCC phenotypes can reduce bias due to ascertainment and missing genotype information as well as provide estimates of absolute and relative risks.</p

Fishing for complementarities : competitive research funding and research productivity

This paper empirically investigates complementarities between different sources of research funding with regard to academic publishing. We find for a sample of UK engineering academics that competitive funding is associated with an increase in ex-post publications but that industry funding decreases the marginal utility of public funding by lowering the publication and citation rate increases associated with public grants. However, when holding all other explanatory variables at their mean, the negative effect of the interaction does not translate into an effective decrease in publication and citation numbers. The paper also shows that the positive effect of public funding is driven by UK research council and charity grants and that EU funding has no significant effect on publication outcomes