Relations between some invariants of algebraic varieties in positive characteristic

We discuss relations between certain invariants of varieties in positive characteristic, like the a-number and the height of the Artin-Mazur formal group. We calculate the a-number for Fermat surfacesComment: 13 page

The Tate conjecture for K3 surfaces over finite fields

Artin's conjecture states that supersingular K3 surfaces over finite fields have Picard number 22. In this paper, we prove Artin's conjecture over fields of characteristic p>3. This implies Tate's conjecture for K3 surfaces over finite fields of characteristic p>3. Our results also yield the Tate conjecture for divisors on certain holomorphic symplectic varieties over finite fields, with some restrictions on the characteristic. As a consequence, we prove the Tate conjecture for cycles of codimension 2 on cubic fourfolds over finite fields of characteristic p>3.Comment: 20 pages, minor changes. Theorem 4 is stated in greater generality, but proofs don't change. Comments still welcom

European integration assessed in the light of the 'rules vs. standards debate'

The interplay of various legal systems in the European Union (EU) has long triggered a debate on the tension between uniformity and diversity of Member States' (MS) laws. This debate takes place among European legal scholars and is also paralleled by economic scholars, e.g. in the ambit of the 'theory of federalism'. This paper takes an innovative perspective on the discrepancy between 'centralized' and 'decentralized' law-making in the EU by assessing it with the help of the rules versus standards debate. When should the EU legislator grant the national legislator leeway in the formulation of new laws and when should all be fixed ex ante at European level? The literature on the 'optimal shape of legal norms' shall be revisited in the light of law-making in the EU, centrally dealing with the question how much discretion shall be given to the national legislator; and under which circumstances. This paper enhances the established decisive factors for the choice of a rule or a standard in a national setting (complexity, volatility, judges' specialization and frequency of application) by two new crucial factors (switching costs and the benefit of uniformity in terms of information costs) in order to assess law-making policies at EU level

On the pp-supports of a holonomic D\mathcal{D}-module

For a smooth variety $Y$ over a perfect field of positive characteristic, the sheaf $D_Y$ of crystalline differential operators on $Y$ (also called the sheaf of $PD$-differential operators) is known to be an Azumaya algebra over $T^*_{Y'},$ the cotangent space of the Frobenius twist $Y'$ of $Y.$ Thus to a sheaf of modules $M$ over $D_Y$ one can assign a closed subvariety of $T^*_{Y'},$ called the $p$-support, namely the support of $M$ seen as a sheaf on $T^*_{Y'}.$ We study here the family of $p$-supports assigned to the reductions modulo primes $p$ of a holonomic $\mathcal{D}$-module. We prove that the Azumaya algebra of differential operators splits on the regular locus of the $p$-support and that the $p$-support is a Lagrangian subvariety of the cotangent space, for $p$ large enough. The latter was conjectured by Kontsevich. Our approach also provides a new proof of the involutivity of the singular support of a holonomic $\mathcal{D}$-module, by reduction modulo $p.$Comment: The article has been rewritten with much improved exposition as well as some additional results, e.g. Corollary 6.3.1. This is the final version, accepted for publication in Inventiones Mathematica

Understanding and protecting vulnerable financial consumers

This article considers how consumer protection law and policy should address the interests of particularly vulnerable financial consumers. Specifically, the article proposes a taxonomy of vulnerability which helps to identify (a) what makes consumers particularly vulnerable, and (b) how consumer protection law and consumer policy (broadly understood) can respond to these causes in a way that provides such consumers with appropriate protection. Changes to economic conditions, legal requirements on traders and our understanding of consumer behaviour make discussion of these issues particularly topical. There is little doubt that finding solutions is extremely difficult. Trade-offs are necessary and some enduring factors that contribute to vulnerability, in particular poverty, sometimes appear intractable. Nevertheless, it is submitted that by identifying clearly both why consumers are vulnerable and how the factors that lead to such vulnerability can be addressed, it is possible to construct an environment which respects consumer choice while ensuring that the most vulnerable are protected appropriately

Regulatory Constructivism: Application of Q Methodology in Italy and China

Conventional view holds that beliefs play an important role in the development of regulations but there is little evidence to support this claim. We use Comparative Q Methodology to systematically map out and compare the beliefs of public officers in China and Italy, two countries with contrasting sets of institutions but have both adopted similar ideas about integrated water resource management. We find some similarities and differences in the beliefs of public officers in both countries. In particular, we find that in both countries beliefs on the regulation of water utilities are diverse and fragmented on issues such as ownership structure of water utilities, how water infrastructure development should be funded, and how tariffs should be regulated. Our findings have two implications for theory, methods and practice. First, the Q methodology is a useful tool for systematically mapping out the beliefs of regulators and managers. Second, systematically mapping out beliefs will help facilitate the development of an alternative regime of regulation such as negotiated rule making. This alternative regime can provide substantial benefits such as more efficient rule making, more cost effective enforcement and compliance, and more equitable in terms of balancing the interests of stakeholders

The reliability of product-specific eco-labels as an agrobiodiversity management instrument

This paper seeks to understand why multinationals prefer to launch a label specific to their own product and examines how reliable these product-specific eco-labels are. A new methodology is applied to assess the extent to which eco-labels live up to claims about their contribution to conservation and the sustainable use of agricultural biodiversity. Product-specific eco-labels are considered as industry self-regulation and all three regulatory stages are studied: the planning, implementation and outcome stage. There are major differences between the product specific eco-labels in the degree in which agrobiodiversity management is part of the normative labeling schemes. Although there are some problems of reliability, such as transparency in the implementation stage and the monitoring in the outcome stage, the degree of reliability of product-specific labels is comparable with eco-labels of international labeling families. The conclusion is that only one of the product-specific eco-labels examined here is reliable when examined in the light of all three stages. The main reason why multinationals establish a product-specific eco-label instead of adopting one from an existing labeling family is that they want to profile themselves as distinct from other companies. The unique character of a product-specific label creates a market opportunity for them

Adult Type 3 Adenylyl Cyclase–Deficient Mice Are Obese

Background: A recent study of obesity in Swedish men found that polymorphisms in the type 3 adenylyl cyclase (AC3) are associated with obesity, suggesting the interesting possibility that AC3 may play a role in weight control. Therefore, we examined the weight of AC3 mice over an extended period of time. Methodology/Principal Findings: We discovered that AC3 2/2 mice become obese as they age. Adult male AC3 2/2 mice are about 40 % heavier than wild type male mice while female AC3 2/2 are 70 % heavier. The additional weight of AC3 2/2 mice is due to increased fat mass and larger adipocytes. Before the onset of obesity, young AC3 2/2 mice exhibit reduced physical activity, increased food consumption, and leptin insensitivity. Surprisingly, the obesity of AC3 2/2 mice is not due to a loss of AC3 from white adipose and a decrease in lipolysis. Conclusions/Significance: We conclude that mice lacking AC3 exhibit obesity that is apparently caused by low locomotor activity, hyperphagia, and leptin insensitivity. The presence of AC3 in primary cilia of neurons of the hypothalamus suggests that cAMP signals generated by AC3 in the hypothalamus may play a critical role in regulation of body weight

Exploitation of the Toll-like receptor system in cancer: a doubled-edged sword?

The toll-like receptor (TLR) system constitutes a pylogenetically ancient, evolutionary conserved, archetypal pattern recognition system, which underpins pathogen recognition by and activation of the immune system. Toll-like receptor agonists have long been used as immunoadjuvants in anti cancer immunotherapy. However, TLRs are increasingly implicated in human disease pathogenesis and an expanding body of both clinical and experimental evidence suggests that the neoplastic process may subvert TLR signalling pathways to advance cancer progression. Recent discoveries in the TLR system open a multitude of potential therapeutic avenues. Extrapolation of such TLR system manipulations to a clinical oncological setting demands care to prevent potentially deleterious activation of TLR-mediated survival pathways. Thus, the TLR system is a double-edge sword, which needs to be carefully wielded in the setting of neoplastic disease