Triangulated categories of mixed motives

This book discusses the construction of triangulated categories of mixed motives over a noetherian scheme of finite dimension, extending Voevodsky's definition of motives over a field. In particular, it is shown that motives with rational coefficients satisfy the formalism of the six operations of Grothendieck. This is achieved by studying descent properties of motives, as well as by comparing different presentations of these categories, following and extending insights and constructions of Deligne, Beilinson, Bloch, Thomason, Gabber, Levine, Morel, Voevodsky, Ayoub, Spitzweck, R\"ondigs, {\O}stv{\ae}r, and others. In particular, the relation of motives with $K$-theory is addressed in full, and we prove the absolute purity theorem with rational coefficients, using Quillen's localization theorem in algebraic $K$-theory together with a variation on the Grothendieck-Riemann-Roch theorem. Using resolution of singularities via alterations of de Jong-Gabber, this leads to a version of Grothendieck-Verdier duality for constructible motivic sheaves with rational coefficients over rather general base schemes. We also study versions with integral coefficients, constructed via sheaves with transfers, for which we obtain partial results. Finally, we associate to any mixed Weil cohomology a system of categories of coefficients and well behaved realization functors, establishing a correspondence between mixed Weil cohomologies and suitable systems of coefficients. The results of this book have already served as ground reference in many subsequent works on motivic sheaves and their realizations, and pointers to the most recent developments of the theory are given in the introduction.Comment: This is the final version. To appear in the series Springer Monographs in Mathematic

Mixed Weil cohomologies

We define, for a regular scheme $S$ and a given field of characteristic zero \KK, the notion of \KK-linear mixed Weil cohomology on smooth $S$-schemes by a simple set of properties, mainly: Nisnevich descent, homotopy invariance, stability (which means that the cohomology of \GG_{m} behaves correctly), and K\"unneth formula. We prove that any mixed Weil cohomology defined on smooth $S$-schemes induces a symmetric monoidal realization of some suitable triangulated category of motives over $S$ to the derived category of the field \KK. This implies a finiteness theorem and a Poincar\'e duality theorem for such a cohomology with respect to smooth and projective $S$-schemes (which can be extended to smooth $S$-schemes when $S$ is the spectrum of a perfect field). This formalism also provides a convenient tool to understand the comparison of such cohomology theories. Our main examples are algebraic de Rham cohomology and rigid cohomology, and the Berthelot-Ogus isomorphism relating them.Comment: update references; hopefully improve the expositio

Verifying privacy by little interaction and no process equivalence

While machine-assisted verification of classical security goals such as confidentiality and authentication is well-established, it is less mature for recent ones. Electronic voting protocols claim properties such as voter privacy. The most common modelling involves indistinguishability, and is specified via trace equivalence in cryptographic extensions of process calculi. However, it has shown restrictions. We describe a novel model, based on unlinkability between two pieces of information. Specifying it as an extension to the Inductive Method allows us to establish voter privacy without the need for approximation or session bounding. The two models and their latest specifications are contrasted

Holistic analysis of mix protocols

Security protocols are often analysed in isolation as academic challenges. However, the real world can require various combinations of them, such as a certified email protocol executed over a resilient channel, or the key registration protocol to precede the purchase protocols of Secure Electronic Transactions (SET). We develop what appears to be the first scalable approach to specifying and analysing mix protocols. It expands on the Inductive Method by exploiting the simplicity with which inductive definitions can refer to each other. This lets the human analyst study each protocol separately first, and then derive holistic properties about the mix. The approach, which is demonstrated on the sequential composition of a certification protocol with an authentication one, is not limited by the features of the protocols, which can, for example, share message components such as cryptographic keys and nonces. It bears potential for the analysis of complex protocols constructed by general composition of others

Inductive analysis of security protocols in Isabelle/HOL with applications to electronic voting

Security protocols are predefined sequences of message exchanges. Their uses over computer networks aim to provide certain guarantees to protocol participants. The sensitive nature of many applications resting on protocols encourages the use of formal methods to provide rigorous correctness proofs. This dissertation presents extensions to the Inductive Method for protocol verification in the Isabelle/HOL interactive theorem prover. The current state of the Inductive Method and of other protocol analysis techniques are reviewed. Protocol composition modelling in the Inductive Method is introduced and put in practice by holistically verifying the composition of a certification protocol with an authentication protocol. Unlike some existing approaches, we are not constrained by independence requirements or search space limitations. A special kind of identity-based signatures, auditable ones, are specified in the Inductive Method and integrated in an analysis of a recent ISO/IEC 9798-3 protocol. A side-by-side verification features both a version of the protocol with auditable identity-based signatures and a version with plain ones. The largest part of the thesis presents extensions for the verification of electronic voting protocols. Innovative specification and verification strategies are described. The crucial property of voter privacy, being the impossibility of knowing how a specific voter voted, is modelled as an unlinkability property between pieces of information. Unlinkability is then specified in the Inductive Method using novel message operators. An electronic voting protocol by Fujioka, Okamoto and Ohta is modelled in the Inductive Method. Its classic confidentiality properties are verified, followed by voter privacy. The approach is shown to be generic enough to be re-usable on other protocols while maintaining a coherent line of reasoning. We compare our work with the widespread process equivalence model and examine respective strengths

Purchasing Key Information Systems The Bord Gais Eireann (BGE) Case

Senior managers have become aware that the management of the information system portfolio of their organisation can ultimately lead to success or failure. The successful selection of mission-critical information systems begins with an understanding of the external and internal business environment and of the technological environment. Many organisations have failed to reap the benefits of their IT investments because they never achieved the required level of integration and cohesiveness between business and IT. The resultant information systems fail to meet the business requirements of the organisation because system requirements are either ill-scoped or the selection process they followed is not business driven. In this paper, the case of Bord Gais Eireann is used to examine the process of selection of a mission-critical system. The paper outlines the specificities of such IS projects and their implications for project management. As a conclusion, the paper puts forward a process model outlining how the integration of business and IT can be achieved to ensure the successful completion of selection stage of IS projects involving the purchase of mission-critical off-the-shelf packages

Attentional and Semantic Anticipations

Why are attentional processes important in the driving of anticipations? Anticipatory processes are fundamental cognitive abilities of living systems, in order to rapidly and accurately perceive new events in the environment, and to trigger adapted behaviors to the newly perceived events. To process anticipations adapted to sequences of various events in complex environments, the cognitive system must be able to run specific anticipations on the basis of selected relevant events. Then more attention must be given to events potentially relevant for the living system, compared to less important events. What are useful attentional factors in anticipatory processes? The relevance of events in the environment depend on the effects they can have on the survival of the living system. The cognitive system must then be able to detect relevant events to drive anticipations and to trigger adapted behaviors. The attention given to an event depends on i) its external physical relevance in the environment, such as time duration and visual quality, and ii) on its internal semantic relevance in memory, such as knowledge about the event (semantic field in memory) and anticipatory power (associative strength to anticipated associates). How can we model interactions between attentional and semantic anticipations? Specific types of distributed recurrent neural networks are able to code temporal sequences of events as associated attractors in memory. Particular learning protocol and spike rate transmission through synaptic associations allow the model presented to vary attentionally the amount of activation of anticipations (by activation or inhibition processes) as a function of the external and internal relevance of the perceived events. This type of model offers a unique opportunity to account for both anticipations and attention in unified terms of neural dynamics in a recurrent network

VANET Applications: Hot Use Cases

Current challenges of car manufacturers are to make roads safe, to achieve free flowing traffic with few congestions, and to reduce pollution by an effective fuel use. To reach these goals, many improvements are performed in-car, but more and more approaches rely on connected cars with communication capabilities between cars, with an infrastructure, or with IoT devices. Monitoring and coordinating vehicles allow then to compute intelligent ways of transportation. Connected cars have introduced a new way of thinking cars - not only as a mean for a driver to go from A to B, but as smart cars - a user extension like the smartphone today. In this report, we introduce concepts and specific vocabulary in order to classify current innovations or ideas on the emerging topic of smart car. We present a graphical categorization showing this evolution in function of the societal evolution. Different perspectives are adopted: a vehicle-centric view, a vehicle-network view, and a user-centric view; described by simple and complex use-cases and illustrated by a list of emerging and current projects from the academic and industrial worlds. We identified an empty space in innovation between the user and his car: paradoxically even if they are both in interaction, they are separated through different application uses. Future challenge is to interlace social concerns of the user within an intelligent and efficient driving