Rational points and non-anticanonical height functions

A conjecture of Batyrev and Manin predicts the asymptotic behaviour of rational points of bounded height on smooth projective varieties over number fields. We prove some new cases of this conjecture for conic bundle surfaces equipped with some non-anticanonical height functions. As a special case, we verify these conjectures for the first time for some smooth cubic surfaces for height functions associated to certain ample line bundles.Comment: 16 pages; minor corrections; Proceedings of the American Mathematical Society, 147 (2019), no. 8, 3209-322

Rational points of bounded height on general conic bundle surfaces

A conjecture of Manin predicts the asymptotic distribution of rational points of bounded height on Fano varieties. In this paper we use conic bundles to obtain correct lower bounds or a wide class of surfaces over number fields for which the conjecture is still far from being proved. For example, we obtain the conjectured lower bound of Manin's conjecture for any del Pezzo surface whose Picard rank is sufficiently large, or for arbitrary del Pezzo surfaces after possibly an extension of the ground field of small degree.Comment: 35 pages; final versio

DOC trail: soil organic matter quality and soil aggregate stability in organic and conventional soils

Conclusion Soil organic matter quality is affected by the agricultural systems of the DOC trial. System effects on the chemical composition, however, were smaller than those on the living organisms in soil and their functions. A close correlation was found between soil structure and microbial biomass indicating that microbes are playing an important role in soil structural stability

Frequency Of Development Of Connective Tissue Disease In Statin-Users Versus Nonusers

Statins have pleiotropic properties that may affect the development of connective tissue diseases (CTD). The objective of this study was to compare the risk of CTD diagnoses in statin users and nonusers. This study was a propensity score-matched analysis of adult patients (30 to 85 years old) in the San Antonio military medical community. The study was divided into baseline (October 1, 2003 to September 30, 2005), and follow-up (October 1, 2005 to March 5, 2010) periods. Statin users received a statin prescription during fiscal year 2005. Nonusers did not receive a statin at any time during the study. The outcome measure was the occurrence of 3 diagnosis codes of the International Classification of Diseases, 9th Revision, Clinical Modification consistent with CTD. We described co-morbidities during the baseline period using the Charlson Comorbidity Index. We created a propensity score based on 41 variables. We then matched statin users and nonusers 1:1, using a caliper of 0.001. Of 46,488 patients who met study criteria (13,640 statin users and 32,848 nonusers), we matched 6,956 pairs of statin users and nonusers. Matched groups were similar in terms of patient age, gender, incidence of co-morbidities, total Charlson Comorbidity Index, health care use, and medication use. The odds ratio for CTD was lower in statin users than nonusers (odds ratio: 0.80; 95% confidence interval: 0.64 to 0.99; p = 0.05). Secondary analysis and sensitivity analysis confirmed these results. In conclusion, statin use was associated with a lower risk of CTD. Published by Elsevier Inc.Pharmac

Number fields with prescribed norms

We study the distribution of extensions of a number field $k$ with fixed abelian Galois group $G$, from which a given finite set of elements of $k$ are norms. In particular, we show the existence of such extensions. Along the way, we show that the Hasse norm principle holds for $100\%$ of $G$-extensions of $k$, when ordered by conductor. The appendix contains an alternative purely geometric proof of our existence result.Comment: 35 pages, comments welcome

The Hasse norm principle for abelian extensions

We study the distribution of abelian extensions of bounded discriminant of a number field k which fail the Hasse norm principle. For example, we classify those finite abelian groups G for which a positive proportion of G-extensions of k fail the Hasse norm principle. We obtain a similar classification for the failure of weak approximation for the associated norm one tori. These results involve counting abelian extensions of bounded discriminant with infinitely many local conditions imposed, which we achieve using tools from harmonic analysis, building on work of Wright

Number fields with prescribed norms

We study the distribution of extensions of a number field k with fixed abelian Galois group G, from which a given finite set of elements of k are norms. In particular, we show the existence of such extensions. Along the way, we show that the Hasse norm principle holds for 100% of G-extensions of k, when ordered by conductor. The appendix contains an alternative purely geometric proof of our existence result

Distribution of genus numbers of abelian number fields

We study the quantitative behaviour of genus numbers of abelian extensions of number fields with given Galois group. We prove an asymptotic formula for the average value of the genus number and show that any given genus number appears only 0% of the time.Comment: 19 pages. Comments welcome