个人简介 魏达盛，男，1978/1/20出生，副高级，
研究方向是数论和算术几何，主要感兴趣的对象是代数簇上有理点和整点的存在性以及一些相关的问题。
教育经历：
2000/09-2005/06 中国科技大学，数学系 博士
1996/09-2000/06 中国科技大学，数学系 学士
工作经历
2017/03-至今 中科院数学与系统科学研究院 研究员
2011/03-2017/03 中科院数学与系统科学研究院 副研究员
2007/07-2011/03 中科院数学与系统科学研究院 助理研究员
2005/07-2007/07 中科院数学与系统科学研究院 博士后

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研究方向 数论

算术几何

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学术论文 C. Liu, D. Wei, L-functions of Witt coverings, Math. Z. 255 (2007), 95-115 L-functions Exponential sums Newton polygon .

C. Ji, D. Wei, On the number of certain Galois extensions of local fields, Proc. Amer. Math. Soc. 135 (2007), 3041-3047 In this paper, we will calculate the number of Galois extensions of local fields with Galois group $A_{n}$ or $S_{n}$ .

C. Ji, D. Wei, Sums of integral squares in cyclotomic fields, C. R. Acad. Sci. Paris, 344 (2007), 413-416

D. Wei, F. Xu, Tower of the maximal abelian extensions of local fields and its application, Manuscripta Math. 129 (2009),1-28 In this paper, we study the algebraic structure of principal units in the tower of the maximal abelian extensions of local fields of characteristic zero and the corresponding Galois groups at each level. As an application, we show the finiteness result for the number of coverings with a given degree of the maximal abelian extension of a local field in characteristic zero. The number of p-coverings for Qp is computed explicitly.

D. Wei, F. Xu, Integral points for multi-norm tori, Proc. Lond. Math. Soc. 104 (2012), no.5, 642–663 We construct a finite subgroup of Brauer–Manin obstruction for detecting the existence of integral points on integral models of principle homogeneous spaces of multi-norm tori. Several explicit examples are provided.

D. Wei, F. Xu, Integral points for groups of multiplicative type, Adv. Math. 232 (2013), no. 1,36-56 Integral point Linear algebraic group of multiplicative type Galois cohomology Brauer–Manin obstruction Strong approximation Sum of two squares

C. Demarche, D. Wei, Hasse principle and weak approximation for multinorm equations, Israel J. Math., 202 (2014), 275–293.

U. Derenthal, D. Wei, Strong approximation and descent, J. Reine Angew. Math. (Crelle) ),731 (2017), 235-258. 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)=N_{K/k}(z): firstly for quartic extensions of number fields K/k and quadratic polynomials P(t) in one variable, and secondly for k=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.

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联系方式 北京市海淀区中关村东路55号数学与系统科学研究院
(+86)
dshwei@amss.ac.cn

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