Shane Kelly

Tight sets and m-ovoids of finite polar spaces

An intriguing set of points of a generalised quadrangle was introduced in [J. Bamberg, M. Law, T. Penttila, Tight sets and m-ovoids of generalised quadrangles, Combinatorica, in press] as a unification of the pre-existing notions of tight set and m-ovoid. It was shown in [J. Bamberg, M. Law, T. Penttila, Tight sets and m-ovoids of generalised quadrangles, Combinatorica, in press] that every intriguing set of points in a finite generalised quadrangle is a tight set or an m-ovoid (for some m). Moreover, it was shown that an m-ovoid and an i-tight set of a common generalised quadrangle intersect in mi points. These results yielded new proofs of old results, and in this paper, we study the natural analogue of intriguing sets in finite polar spaces of higher rank. In particular, we use the techniques developed in this paper to give an alternative proof of a result of Thas [J.A. Thas, Ovoids and spreads of finite classical polar spaces, Geom. Dedicata 10 (1-4) (1981) 135-143] that there are no ovoids of H(2r,q^2), Q^-(2r+1,q), and W(2r-1,q) for r>2. We also strengthen a result of Drudge on the non-existence of tight sets in W(2r-1,q), H(2r+1,q^2), and Q^+(2r+1,q), and we give a new proof of a result of De Winter, Luyckx, and Thas [S. De Winter, J.A. Thas, SPG-reguli satisfying the polar property and a new semipartial geometry, Des. Codes Cryptogr. 32 (1-3) (2004) 153-166; D. Luyckx, m-Systems of finite classical polar spaces, PhD thesis, The University of Ghent, 2002] that an m-system of W(4m+3,q) or Q^-(4m+3,q) is a pseudo-ovoid of the ambient projective space.

Is there an association between chronic lung disease and abdominal aortic aneurysm expansion

Background:  Although there is evidence demonstrating an association between chronic obstructive pulmonary disease (COPD) and abdominal aortic aneurysm (AAA), it is not clear whether COPD predicts greater rates of expansion of established aneurysms. We sought such an association in a cohort of men with aneurysms detected in a population‐based study of screening for aneurysms.

Vanishing of negative -theory in positive characteristic

We show how a theorem of Gabber on alterations can be used to apply the work of Cisinski, Suslin, Voevodsky, and Weibel to prove that

Constructions of intriguing sets of polar spaces from field reduction and derivation

K_n(X) \otimes \mathbb{Z}[{1}/{p}]= 0

Differential forms in positive characteristic, II :cdh-descent via functorial Riemann–Zariski spaces

for

Triangulated categories of motives in positive characteristic

n < {-}\! \dim X

The motivic Steenrod algebra in positive characteristic

where

Points in algebraic geometry

X

Differential forms in positive characteristic avoiding resolution of singularities

is a quasi-excellent noetherian scheme,

Weight Homology of Motives

p