Details
| Original language | English |
|---|---|
| Pages (from-to) | 235-258 |
| Number of pages | 24 |
| Journal | Journal fur die Reine und Angewandte Mathematik |
| Volume | 2017 |
| Issue number | 731 |
| Publication status | Published - Oct 2017 |
Abstract
We introduce descent methods to the study of strong approximation on algebraic varieties. We apply them to two classes of varieties defined by P(t) = NK/κ(z): firstly for quartic extensions of number fields K/κ and quadratic polynomials P(t) in one variable, and secondly for κ = ℚ, an arbitrary number field K and P(t) a product of linear polynomials over ℚ in at least two variables. Finally, we illustrate that a certain unboundedness condition at archimedean places is necessary for strong approximation.
ASJC Scopus subject areas
- Mathematics(all)
- Mathematics(all)
- Applied Mathematics
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In: Journal fur die Reine und Angewandte Mathematik, Vol. 2017, No. 731, 10.2017, p. 235-258.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Strong approximation and descent
AU - Derenthal, Ulrich
AU - Wei, Dasheng
N1 - Funding information: The first author was supported by the Deutsche Forschungsgemeinschaft (Grant No. DE 1646/2-1 and DE 1646/3-1). The second author is supported by National Key Basic Research Program of China (Grant No. 2013CB834202) and National Natural Science Foundation of China (Grant No. 11371210 and 11321101).
PY - 2017/10
Y1 - 2017/10
N2 - We introduce descent methods to the study of strong approximation on algebraic varieties. We apply them to two classes of varieties defined by P(t) = NK/κ(z): firstly for quartic extensions of number fields K/κ and quadratic polynomials P(t) in one variable, and secondly for κ = ℚ, an arbitrary number field K and P(t) a product of linear polynomials over ℚ in at least two variables. Finally, we illustrate that a certain unboundedness condition at archimedean places is necessary for strong approximation.
AB - We introduce descent methods to the study of strong approximation on algebraic varieties. We apply them to two classes of varieties defined by P(t) = NK/κ(z): firstly for quartic extensions of number fields K/κ and quadratic polynomials P(t) in one variable, and secondly for κ = ℚ, an arbitrary number field K and P(t) a product of linear polynomials over ℚ in at least two variables. Finally, we illustrate that a certain unboundedness condition at archimedean places is necessary for strong approximation.
UR - http://www.scopus.com/inward/record.url?scp=85032276807&partnerID=8YFLogxK
U2 - 10.1515/crelle-2014-0149
DO - 10.1515/crelle-2014-0149
M3 - Article
AN - SCOPUS:85032276807
VL - 2017
SP - 235
EP - 258
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
SN - 0075-4102
IS - 731
ER -