Research / Science / Development

As in other societal realms also in research, science, and development governments and parliaments increasingly have to legitimize their actions and want to base their future activities on informed decisions. Consequently, performance measures, benchmarking, comparative analysis, “foresight studies” are increasingly asked for. Ranking, ratings and evaluations are introduced throughout the system supposedly providing on the one hand the requested transparency and at the same time acting as stimuli to improve the performance. However, to date central questions relating to the underlying methodologies and indicators used are unanswered. These questions concern the availability and appropriateness of the data, indicator construction and methodologies on the one hand, tackle issues as how to deal with effects due to disciplinary, sectoral, regional or national differences, and concern the intended and unintended effects of the instruments used. In the contribution these issues are described and discussed in more detail. In Germany so far infrastructural deficiencies e.g. the fragmentation of research groups addressing those issues prevent adequately addressing the open research questions. Behind this background the two most important tasks identified are them the development of a decentralized data collection system enabling standard definitions and the development of a competitive research infrastructure.Science Indicators, R&D, Research Funding, Governance

Beta-elements and divided congruences

The f-invariant is an injective homomorphism from the 2-line of the Adams-Novikov spectral sequence to a group which is closely related to divided congruences of elliptic modular forms. We compute the f-invariant for two infinite families of beta-elements and explain the relation of the arithmetic of divided congruences with the Kervaire invariant one problem.Comment: minor changes; final version, to appear in Amer. J. Mat

Schubert calculus for algebraic cobordism

We establish a Schubert calculus for Bott-Samelson resolutions in the algebraic cobordism ring of a complete flag variety G/B.Comment: 27 pages, Appendix added, slightly abridged version to appear in Crell

On non-commutative twisting in etale and motivic cohomology

In this paper we use ideas of the non-abelian Iwasawa main conjecture to prove a result about the first Galois cohomology of continuous Galois modules V_p(j) for large Tate-twist j and V_p a Q_p vector space. We show that under a technical hypothesis that H^1(K, V_p(j)) is generated by twists of norm-compatible units in an infinite tower of number fields with elements in V_p(j-1). This confirms a consequence of the non-abelian Iwasawa main conjecture. Using the "Bloch-Kato-conjecture" a similar result is proven for motivic cohomology with finite coefficients.Comment: 22 page