1,585 research outputs found
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
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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 with fixed
abelian Galois group , from which a given finite set of elements of are
norms. In particular, we show the existence of such extensions. Along the way,
we show that the Hasse norm principle holds for of -extensions of
, 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
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