A quantitative sharpening of Moriwaki's arithmetic Bogomolov inequality

A. Moriwaki proved the following arithmetic analogue of the Bogomolov unstability theorem. If a torsion-free hermitian coherent sheaf on an arithmetic surface has negative discriminant then it admits an arithmetically destabilising subsheaf. In the geometric situation it is known that such a subsheaf can be found subject to an additional numerical constraint and here we prove the arithmetic analogue. We then apply this result to slightly simplify a part of C. Soul\'e's proof of a vanishing theorem on arithmetic surfaces.Comment: final version, to appear in Math. Res. Let

Some aspects of the ecology of the limnoplankton, with special reference to the phytoplankton. [Translation from: Svensk Botanisk Tidskrift 13(2) 129-163, 1919.]

This paper tries to develop more generally some fundamental bases for the ecological study of freshwater plankton. A special attention is given to the phytoplankton associations which can be separated out and made into groups according to their dependence upon changing environments. Plankton formations in different types of water bodies (ponds, lakes and rivers) are studied

Arithmetically defined dense subgroups of Morava stabilizer groups

For every prime $p$ and integer $n\ge 3$ we explicitly construct an abelian variety A/\F_{p^n} of dimension $n$ such that for a suitable prime $l$ the group of quasi-isogenies of A/\F_{p^n} of $l$-power degree is canonically a dense subgroup of the $n$-th Morava stabilizer group at $p$. We also give a variant of this result taking into account a polarization. This is motivated by a perceivable generalization of topological modular forms to more general topological automorphic forms. For this, we prove some results about approximation of local units in maximal orders which is of independent interest. For example, it gives a precise solution to the problem of extending automorphisms of the $p$-divisible group of a simple abelian variety over a finite field to quasi-isogenies of the abelian variety of degree divisible by as few primes as possible.Comment: major revision, main results slightly changed; final version, to appear in Compositio Mat

Probing QCD Parameters with Top-Quark Data

Results from inclusive and differential measurements of the production cross sections for top quarks in proton-proton collisions at center-of-mass energies of 7 and 8 TeV are compared to predictions at next-to-leading and next-to-next-to-leading order in perturbative Quantum Chromodynamics. From these studies, constraints on the top-quark mass, the strong coupling constant, and on parton distributions functions are determined.Comment: 8 pages, 11 figures, to appear in the proceedings of the 6th International Workshop on Top Quark Physics (TOP2013