Pour X une courbe sur un corps global k, lisse, projective et géométriquement connexe, nous déterminons la Q-structure du groupe de Quillen K1(X) : nous démontrons que dimQ K1(X) ? Q =2r, où r désigne le nombre de places archimédiennes de k (y compris le cas r = 0 pour un corps de fonctions). Cela con?rme une conjecture de Bloch annoncée dans les années 1980. Dans le langage de la K-théorie de Milnor, que nous dé?nissons pour les variétés algébriques via les groupes de Somekawa, le premier K-groupe spécial de Milnor SKM1 (X) est de torsion. Pour la preuve, nous développons une théorie des hauteurs applicable aux K-groupes de Milnor, et nous généralisons l’approche de base de facteurs de Bass-Tate. Une structure plus ?ne de SKM 1 (X) émerge en localisant le corps de base k, et une description explicite de la décomposition correspondante est donnée. En particulier, nous identi?ons un sous-groupe WKl(X):= ker (SKM 1 (X) ? Zl ? Lv SKM 1 (Xv) ? Zl) pour chaque entier rationnel l, nommé noyau sauvage, dont nous croyons qu’il est ?ni. / For a smooth projective geometrically connected curve X over a global ?eld k, we determine the Q-structure of its ?rst Quillen K-group K1(X) by showing that dimQ K1(X) ? Q =2r, where r denotes the number of archimedean places of k (including the case r = 0 for k a function ?eld). This con?rms a conjecture of Bloch. In the language of Milnor K-theory, which we de?ne for varieties via Somekawa groups, the ?rst special Milnor K-group SKM 1 (X) is torsion. For the proof, we develop a theory of heights applicable to Milnor K-groups, and generalize the factor basis approach of Bass-Tate. A ?ner structure of SKM 1 (X) emerges when localizing the ground ?eld k, and we give an explicit description of the resulting decomposition. In particular, we identify a potentially ?nite subgroup WKl(X):= ker (SKM 1 (X) ? Zl ? Lv SKM 1 (Xv) ? Zl) for each rational prime l, named wild kernel.

There has been in the past ten to fifteen years a surge of activity concerning the cohomology of semi-direct product groups of the form $\mathbb{Z}^{n}\rtimes$G with G finite. A problem first stated by Adem-Ge-Pan-Petrosyan asks for suitable conditions for the Lyndon-Hochschild-Serre Spectral Sequence associated to this group extension to collapse at second page of the Lyndon-Hochschild-Serre spectral sequence. In this thesis we use facts from integer representation theory to reduce this problem to only considering representatives from each genus of representations, and establish techniques for constructing new examples in which the spectral sequence collapses.

The irrational rotation algebra A_θ is known to be Poincaré self-dual in the KK-theoretic sense. The spectral triple representing the required K-homology fundamental class was constructed by Connes out of the Dolbeault operator on the 2-torus, but so far, there has not been an explicit description of the dual element. We geometrically construct, for certain elements g of the modular group, a finitely generated projective module L_g over A_θ ⊗ A_θ out of a pair of transverse Kronecker flows on the 2-torus. For upper triangular g, we find an unbounded cycle representing the dual of said module under Kasparov product with Connes' class, and prove that this cycle is invertible in KK(A_θ,A_θ), allowing us to 'untwist' L_g to an unbounded cycle representing the unit for the self-duality of A_θ. / Graduate

<div>This thesis consists of three chapters. In the first chapter, I investigate the effects of complexity in various voting systems on individual behavior in small group electoral competitions. Using a laboratory experiment, I observe individual behavior within one of three voting systems -- plurality, instant runoff voting (IRV), and score then automatic runoff (STAR). I then estimate subjects' behavior in three different models of bounded rationality. The estimated models are a model of Level-K thinking (Nagel, 1995), the Cognitive Hierarchy (CH) model (Camerer, et al. 2004), and a Quantal Response Equilibrium (QRE) (McKelvey and Palfrey 1995). I consistently find that more complex voting systems induce lower levels of strategic thinking. This implies that policy makers desiring more sincere voting behavior could potentially achieve this through voting systems with more complex strategy sets. Of the tested behavioral models, Level-K consistently fits observed data the best, implying subjects make decisions that combine of steps of thinking with random, utility maximizing, errors.</div><div><br></div><div>In the second chapter, I investigate the relationship between the mechanisms used to select leaders and both measures of group performance and leaders' ethical behavior. Using a laboratory experiment, we measure group performance in a group minimum effort task with a leader selected using one of three mechanisms: random, a competition task, and voting. After the group task, leaders must complete a task that asks them to behave honestly or dishonestly in questions related to the groups performance. We find that leaders have a large impact on group performance when compared to those groups without leaders. Evidence for which selection mechanism performs best in terms of group performance seems mixed. On measures of honesty, the strongest evidence seems to indicate that honesty is most positively impacted through a voting selection mechanism, which differences in ethical behavior between the random and competition selection treatments are negligible.</div><div><br></div><div><br></div><div>In the third chapter, I provide an investigation into the factors and conditions that drive "free riding" behavior in dynamic innovation contests. Starting from a dynamic innovation contest model from Halac, et al. (2017), I construct a two period dynamic innovation contest game. From there, I provide a theoretical background and derivation of mixed strategies that can be interpreted as an agent's degree to which they engage in free riding behavior, namely through allowing their opponent to exert effort in order to uncover information about an uncertain state of the world. I show certain conditions must be fulfilled in order to induce free riding in equilibrium, and also analytically show the impact of changing contest prize structures on the degree of free riding. I end this paper with an experimental design to test these various theoretical conclusions in a laboratory setting while also considering the behavioral observations recorded in studies investigating similar contest models and provide a plan to analyze the data collected by this laboratory experiment.</div><div><br></div><div>All data collected for this study consists of individual human subject data collected from laboratory experiments. Project procedures have been conducted in accordance with Purdue's internal review board approval and known consent from all participants was obtained.</div>

En employant des méthodes de la théorie de Chern-Weil, Reznikov produit une condition suffisante qui assure la non-trivialité de la projectivisation \( \mathbb{P}(E) \) d'un fibré vectoriel complexe en tant que fibré Hamiltonien. Dans le contexte de la quantification géométrique, Savelyev et Shelukhin introduisent un nouvel invariant des fibrés Hamiltoniens avec valeurs dans la K-théorie et étendent le résultat de Reznikov. Cet invariant est donné par l'indice d'Atiyah-Singer d'une famille d'opérateurs \( \text{Spin}^{c} \) de Dirac. Dans ce mémoire, on s'intéresse à des fibrés Hamiltoniens résultant d'un produit fibré et d'un produit cartésien d'une collection de fibrés projectifs complexes \( \mathbb{P}(E_1), \cdots, \mathbb{P}(E_r) \). En usant des mêmes méthodes que Shelukhin et Savelyev, on définit une famille d'opérateurs \( \text{Spin}^{c} \) de Dirac qui agissent sur les sections d'un fibré de Dirac canonique à valeurs dans un fibré pré-quantique. L'indice de famille produit un invariant de fibrés Hamiltoniens avec fibres données par un produit d'espaces projectifs complexes et permet de construire des exemples de fibrés Hamiltoniens non-triviaux. / Using methods of Chern-Weil Theory, Reznikov provides a sufficient condition for the non-triviality of the projectivization \( \mathbb{P}(E) \) of a complex vector bundle \( E \) as a Hamiltonian fibration. In the setting of geometric quantization, Savelyev and Shelukhin introduce a new invariant of Hamiltonian fibrations and a K-theoretic lift of Reznikov's result. This invariant is given by the Atiyah-Singer index of a family of \( \text{Spin}^{c} \)-Dirac operators. In this thesis, we consider Hamiltonian fibrations given by the Cartesian product and the fiber product of a collection of complex projective bundles \( \mathbb{P}(E_1), \cdots, \mathbb{P}(E_r) \). Using the same methods as Savelyev and Shelukhin, we define a family of \( \text{Spin}^{c} \)-Dirac operators acting on sections of a canonical Dirac bundle with values in a suitable prequantum fibration. The family index gives then an invariant of Hamiltonian fibrations with fibers given by a product of complex projective spaces and allows to construct examples of non-trivial Hamiltonian fibrations.

We explore motivic homotopy theory over deeper bases than the spectrum of the integers: Starting from a commutative group object in a cartesian closed presentable infinity category, replacing the usual multiplicative group scheme in motivic spaces, we construct projective spaces, and show that infinite dimensional projective space is the classifying space of the group object. After passage to the stabilization, we construct a Snaith spectrum, calculate the cohomology represented by it for projective spaces and on its rationalization produce Adams operations and a splitting into summands of their eigenspaces.

This Ph.D. thesis deals with E1-ring structures on the Hermitian K-theory in the motivic setting, more precisely, the existence of such structures on the motivic spectrum representing the hermitianK-theory is proven. The presence of such structure is established through two different approaches. In both cases, we consider the category of algebraic vector bundles over a scheme, with the usual requirements to do motivic homotopy theory. This category has two natural symmetric monoidal structures given by the direct sum and the tensor product, together with a duality coming from the functor represented by the structural sheaf. The first symmetric monoidal structure is the one that we are going to group complete along this text, and we will see that the second one, the tensor product, is preserved giving rise to an E1-ring structure in the resulting spectrum. In the first case, a classic infinite loop space machine applies to the hermitian category of the category of algebraic vector bundles over a scheme. The second approach abords the construction using a new hermitian infinite loop space machine which uses the language of infinity categories. Both assemblies applied to our original category have like output a presheaf of E1-ring spectra. To get an spectrum representing the hermitian K-theory in the motivic context we need a motivic spectrum, i.e, a P1-spectrum. We use a delooping construction at the end of the text to obtain a presheaf of E1-ring P1-spectra from the two presheaves of E1-ring spectra indicated above.

Le raisonnement de la fertilisation azotée du blé a, depuis 40 ans, été largement orienté par le consensus autour de la méthode du bilan, avec comme principes fondamentaux : une nutrition azotée non limitante tout au long du cycle et l’estimation, de manière indépendante, des différents termes de l’équation du bilan pour caractériser la fourniture du sol et les besoins en azote de la plante. Au regard des enjeux de réduction des pollutions environnementales, de l’évolution des exigences qualitative du marché, ainsi que des difficultés de mise en oeuvre de la méthode, on s’interroge sur l’opportunité de renouveler ce paradigme. Pour proposer une nouvelle méthode qui réponde aux divers enjeux concernant l’azote, qui valorise au mieux les connaissances disponibles et dont la mise en oeuvre est cohérente avec les moyens des acteurs, nous avons mis en oeuvre une démarche de conception innovante, structurée en 3 étapes : un diagnostic des usages des outils actuels, une phase de conception, incluant des ateliers de conception et la mise au point de règle de décision à l’aide d’un modèle, et un test d’usage du prototype conçu.Le diagnostic des usages a mis en évidence plusieurs obstacles à la mise en oeuvre de la méthode du bilan, dont la fixation de l’objectif de rendement, ce qui a orienté la phase de conception vers l’exploration d’un concept de méthode de fertilisation azotée permettant de s’en affranchir. La méthode mise au point est basée sur le suivi régulier de l’état de nutrition azotée de la plante, l’acceptation de carences en azote non préjudiciables et des règles de décision tenant compte des conditions météorologiques au moment de l’apport. Nous montrons que la conception a rendu nécessaire la production de nouvelles connaissances, mais aussi la diversification des ressources et des compétences habituellement mobilisées. Ce travail enrichit les méthodes de conception d’outils d’aide à la décision en montrant comment l’articulation des 3 étapes permet de sortir du paradigme qui domine la fertilisation azotée depuis des décennies et d’élaborer un outil palliant les défauts des outils actuels. / Decisions about nitrogen fertilizer application on wheat have, for the last 40 years, been based on the balance sheet method, with the following underlying principles: non-limiting nitrogen nutrition throughout the crop cycle, and independent estimation of the various terms of the equation, to characterize soil nitrogen supply and plant nitrogen needs. Environmental pollution, changes in the qualitative requirements of the market and difficulties implementing this method have raised questions about whether it might be appropriate to switch to new ways of managing nitrogen fertilizer. We developed a new method meeting the diverse constraints relating to nitrogen use, making the best use of available knowledge and easily applicable by users, through a 3-steps innovative design approach: a diagnosis of the use of current tools, a design phase including design workshops, production of new knowledge, a modelbased prototyping, and the testing of a prototype method.The diagnosis of uses identified several barriers to the implementation of the balance sheet method, including the need to set a target yield. This directed the design phase towards the exploration of new ways of managing nitrogen fertilizer that did not require the fixing of a target yield. The method developed is based on the regular monitoring of plant nitrogen nutrition, the toleration of periods of nitrogen deficiency that are not prejudicial and the use of decision rules taking weather conditions at the time of nitrogen application into account.This design required the generation of new knowledge and a diversification of the resources and skills usually mobilized. This work enriches the methods for designing decision support tools and shows how a combination of 3 steps can be used to develop a tool for managing nitrogen fertilizer applications completely different from the dominant paradigm of the last 40 years, and compensating the defects of current methods.

No description available.

It is argued that the geometric dual of a noncommutative operator algebra represents a notion of quantum state space which differs from existing notions by representing observables as maps from states to outcomes rather than from states to distributions on outcomes. A program of solving for an explicitly geometric manifestation of quantum state space by adapting the spectral presheaf, a construction meant to analyze contextuality in quantum mechanics, to derive simple reconstructions of noncommutative topological tools from their topological prototypes is presented. We associate to each unital C&ast;-algebra A a geometric object--a diagram of topological spaces representing quotient spaces of the noncommutative space underlying A&mdash;meant to serve the role of a generalized Gel'fand spectrum. After showing that any functor F from compact Hausdorff spaces to a suitable target category C can be applied directly to these geometric objects to automatically yield an extension F^&sim; which acts on all unital C&ast;-algebras, we compare a novel formulation of the operator K₀ functor to the extension K^&sim; of the topological K-functor. We then conjecture that the extension of the functor assigning a topological space its topological lattice assigns a unital C&ast;-algebra the topological lattice of its primary ideal spectrum and prove the von Neumann algebraic analogue of this conjecture.