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Contributions to the essential dimension of finite and algebraic groups
Full text linkEssential dimension, introduced by Joe Buhler and Zinovy Reichstein and in its most general form by Alexander Merkurjev is a measure of complexity of algebraic objects such as quadratic forms, hermitian forms, central simple algebras and étale algebras. Informally, the essential dimension of an algebraic object is the number of parameters needed to define it.
Often isomorphism classes of objects of some type are in one to one bijection with isomorphism classes of G-torsors. The maximal essential dimension of a G-torsor (called essential dimension of G) gives an invariant of algebraic groups, which will be of primary interest in this thesis. The text is subdivided into four chapters as follows:
Chapter I+II: Multihomogenization of covariants and its application to covariant and essential dimension
The essential dimension of a linear algebraic group G can be expressed via G-equivariant rational maps phi: A(V) --> A(W), so called covariants, between generically free G-modules V and W. In these two chapters we explore a new technique for dealing with covariants, called multihomogenization. This technique was jointly introduced with Hanspeter Kraft and Gerald Schwarz in an already published paper, which forms the second chapter.
Applications of the multihomogenization technique to the essential dimension of algebraic groups are given by results on the essential dimension of central extensions, direct products, subgroups and the precise relation of essential dimension and covariant dimension (which is a variant of the former with polynomial covariants). Moreover the multihomogenization technique allows one to extend a twisting construction introduced by Matthieu Florence from the case of irreducible representations to completely reducible representations. This relates Florence's work on the essential dimension of cyclic p-groups to recent stack theoretic approaches by Patrick Brosnan, Angelo Vistoli and Zinovy Reichstein and by Nikita Karpenko and Alexander Mekurjev.
Chapter III: Faithful and p-faithful representations of minimal dimension
The study of essential dimension of finite and algebraic groups is closely related to the study of its faithful resp. generically free representations. In general the essential dimension of an algebraic group is bounded above by the least dimension of a generically free representation minus the dimension of the algebraic group. In some prominent cases this upper bound or a variant of it is strict.
In this chapter we are guided by the following general questions: What do faithful representations of the least possible dimension look like? How can they be constructed? How are they related to faithful representations of minimal dimension of subgroups? Along the way we compute the minimal number of irreducible representations needed to construct a faithful representation.
Chapter IV: Essential p-dimension of algebraic tori
This chapter is joint work with Mark MacDonald, Aurel Meyer and Zinovy Reichstein. We study a variant of essential dimension which is relative to a prime number p. This variant, called essential p-dimension, disregards effects resulting from other primes than p. In a recent paper Nikita Karpenko and Alexander Merkurjev have computed the essential dimension of p-groups. We extend their result and find the essential p-dimension for a class of algebraic groups, which includes all algebraic tori and twisted finite p-groups
Birational isomorphisms between twisted group actions
No full textLet X be an algebraic variety with a generically free action of a connected algebraic group G. Given an automorphism phi:G -> G, we will denote by X-phi the same variety X with the G-action given by g:x -> phi(g) (.) x. We construct examples of G-varieties X such that X and X-phi are not Gequivariantly isomorphic. The problem of whether or not such examples can exist in the case where X is a vector space with a generically free linear action, remains open. On the other hand, we prove that X and X-phi are always stably birationally isomorphic, i.e., X x A(m) and X phi x A(m) are G-equivariantly birationally isomorphic for a suitable m >= 0
Physiological and physicochemical controls on foliar volatile organic compound emissions
No full textFuel on the Invention Funnel: Technology Licensing-in, Antecedents, and Invention Performance
No full textIn this paper, we examine the impact of technology licensing-in on firm invention performance. Studying a sample of 266 licensees and matched non-licensees using a two-part model specification, we find that licensees are more likely to introduce inventions than their non-licensee counterparts. This holds both if we consider invention in general, and invention in the licensed technological class only. We also show that familiarity with the licensed technology and technological specialization drives licensees to pursue a narrow invention strategy primarily focusing on the technological class specified in the license agreement
Physiological and physicochemical controls on foliar volatile organic compound emissions
No full textPlant leaves emit a broad spectrum of organic compounds that typically play multiple roles in plant protection. Furthermore, most of these compounds actively
participate in tropospheric chemistry. There has been rapid progress in understanding how the emission of volatiles is regulated, mostly focusing on the biochemical controls over compound production. However, physicochemical characteristics such as low volatility or diffusion can also control the emissions and interact with physiological limitations. In particular, nonspecific
leaf storage of less volatile compounds
smooths the emission responses to fluctuating environmental conditions, and diffusion through stomata leads to conspicuous emission bursts after stomatal opening and modifications of diurnal emission time courses. Because natural conditions always fluctuate, both physiological and physicochemical controls exert a major influence over plant volatile emissions
gdkrmr/summarizing_the_state_of_the_biosphere v1.1.1
No full textCode to reproduce the paper
Kraemer, G., Camps-Valls, G., Reichstein, M., & Mahecha, M. D. (2020). Summarizing the state of the terrestrial biosphere in few dimensions. Biogeosciences, 17(9), 2397–2424. https://doi.org/10.5194/bg-17-2397-2020
if you use this code, please cite the paper
Data sets used in Lee et al. (2023)
No full textModel simulations and processed data sets used in Lee, H., Jung, M., Carvalhais, N., Trautmann, T., Kraft, B., Reichstein, M., Forkel, M., and Koirala, S.: Diagnosing modeling errors of global terrestrial water storage interannual variability, Hydrol. Earth Syst. Sci. Discuss. [preprint], https://doi.org/10.5194/hess-2022-284, in review, 2022
Open innovation, value creation and value capture : an introduction
Full text linkTo be successful in open innovation, firms need to craft an effective strategy for both
value creation and value capture. However, these two aspects are difficult to combine,
and there are important tensions that deserve closer examination. The aim of this special section is to offer original perspectives on key conceptual and empirical research
questions related to how open innovation can help organizations to create and capture
value, the extent to which there might be a tension between value creation and value
capture in open innovation strategies, and how this tension can be effectively dealt
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The environment of AGNs and the activity degree of their surrounding galaxies
No full textAims. We present results of a comprehensive spectral study on the large-scale environment of active galactic nuclei (AGNs) based on Sloan Spectroscopic Survey data.
Methods. We analyzed the spectra of galaxies in the environment of AGN and other activity classes up to distances of 1 Mpc.
Results. The mean Hα and [O ii
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