Principal ideals and smooth curves

AbstractLet A be the coordinate ring of an affine piece of a smooth curve, V, defined over either R or an algebraically closed field k. We ask which maximal ideals of A are principal. We give a complete determination if V has genus 0 or 1, and give partial results if V has genus >/ 2. We conjecture that if k is algebraically closed of characteristic 0, genus (V) >/ 2, then A has only finitely many principal maximal ideals. This conjecture is equivalent to the Mordell Conjecture of Diophantine Geometry

Generalised Moore spectra in a triangulated category

In this paper we consider a construction in an arbitrary triangulated category T which resembles the notion of a Moore spectrum in algebraic topology. Namely, given a compact object C of T satisfying some finite tilting assumptions, we obtain a functor which "approximates" objects of the module category of the endomorphism algebra of C in T. This generalises and extends a construction of Jorgensen in connection with lifts of certain homological functors of derived categories. We show that this new functor is well-behaved with respect to short exact sequences and distinguished triangles, and as a consequence we obtain a new way of embedding the module category in a triangulated category. As an example of the theory, we recover Keller's canonical embedding of the module category of a path algebra of a quiver with no oriented cycles into its u-cluster category for u>1.Comment: 26 pages, improvement to exposition of the proof of Theorem 3.

On the vanishing of negative K-groups

Let k be an infinite perfect field of positive characteristic p and assume that strong resolution of singularities holds over k. We prove that, if X is a d-dimensional noetherian scheme whose underlying reduced scheme is essentially of finite type over the field k, then the negative K-group K_q(X) vanishes for every q < -d. This partially affirms a conjecture of Weibel.Comment: Math. Ann. (to appear

Inhomogeneous Yang-Mills algebras

We determine all inhomogeneous Yang-Mills algebras and super Yang-Mills algebras which are Koszul. Following a recent proposal, a non-homogeneous algebra is said to be Koszul if the homogeneous part is Koszul and if the PBW property holds. In this paper, the homogeneous parts are the Yang-Mills algebra and the super Yang-Mills algebra.Comment: 17 page

Global Dimension of Polynomial Rings in Partially Commuting Variables

For any free partially commutative monoid $M(E,I)$, we compute the global dimension of the category of $M(E,I)$-objects in an Abelian category with exact coproducts. As a corollary, we generalize Hilbert's Syzygy Theorem to polynomial rings in partially commuting variables.Comment: 11 pages, 2 figure

Reducing Computational Costs in the Basic Perturbation Lemma

Homological Perturbation Theory [11, 13] is a well-known general method for computing homology, but its main algorithm, the Basic Perturbation Lemma, presents, in general, high computational costs. In this paper, we propose a general strategy in order to reduce the complexity in some important formulas (those following a specific pattern) obtained by this algorithm. Then, we show two examples of application of this methodology.

An algebraic proof of Bogomolov-Tian-Todorov theorem

We give a completely algebraic proof of the Bogomolov-Tian-Todorov theorem. More precisely, we shall prove that if X is a smooth projective variety with trivial canonical bundle defined over an algebraically closed field of characteristic 0, then the L-infinity algebra governing infinitesimal deformations of X is quasi-isomorphic to an abelian differential graded Lie algebra.Comment: 20 pages, amspro

The K-theoretic Farrell-Jones Conjecture for hyperbolic groups

We prove the K-theoretic Farrell-Jones Conjecture for hyperbolic groups with (twisted) coefficients in any associative ring with unit.Comment: 33 pages; final version; to appear in Invent. Mat

Comparative fruit quality parameters of ‘Ninfa’ apricot (Prunus armeniaca L.) grafted on two different rootstocks in a newly established organic orchard

The fruit quality parameters of Prunus armeniaca L. cv ‘Ninfa’ grafted on ‘Myrobalan 29C’ (Prunus cerasifera Ehrh.) and ‘Real Fino’ apricot seedling (Prunus armeniaca L.) were analysed in an experimental orchard under organic management. The study was performed between 2010 and 2012 in the province of Seville (SW Spain). Colour, fruit and stone weights, firmness, soluble solid concentration, and acidity were measured for fruit quality evaluation. Trunk cross-sectional area, main branches, and fruit yield were also determined. In general, ‘Myrobalan 29C’ rootstock produced fruit slightly larger in size and with a bigger weight. By contrast, apricots on ‘Myrobalan 29C’ had less firmness and a lower solid soluble concentration than on ‘Real Fino’. There was little difference in the colour, acidity, and stone dry weights. Trees on ‘Real Fino’ had larger areas of trunk and branches but no significant differences were obtained in relation to fruit yields

Hermitian K-theory and 2-regularity for totally real number fields

We completely determine the 2-primary torsion subgroups of the hermitian K-groups of rings of 2-integers in totally real 2-regular number fields. The result is almost periodic with period 8. We also identify the homotopy fibers of the forgetful and hyperbolic maps relating hermitian and algebraic K-theory. The result is then exactly periodic of period 8. In both the orthogonal and symplectic cases, we prove the 2-primary hermitian Quillen-Lichtenbaum conjecture.Comment: To appear in Mathematische Annale