报告人： 孙晓松 (北京大学)

题名：Polynomial maps with additive-nilpotent Jacobian matrix
这个报告主要介绍Cohen-Lenstra Conjecture，以及最近Fouvry and Kluners的两篇文章。

摘要:  Several important problems in affine algebraic geometry, such as
the Jacobian Conjecture and the Tame Generators Problem, are closely
related to the research of polynomial automorphisms and derivations on
polynomial algebras. We prove that the Jacobian Conjecture holds for
polynomial maps with so-called ``additive-nilpotent'' Jacobian matrix.
And the structure of these maps are discussed with emphasis on
quadratic automorphisms, in particular we solve the Tame Generators
Problem for quadratic automorphisms in dimension five.

参考资料：
papers
1) H. Bass, E. Connel, D. Wright, The Jacobian Conjecture: Reduction
of degree and formal expansion of the inverse, Bull. Amer. Math. Soc.,
1982, 7(2): 287-330.
2) A. van den Essen, Polynomial automorphisms and the Jacobian
conjecture, Algèbre non commutative, groupes quantiques et invariants
(Reims, 1995), 55-81, Sémin. Congr., 2,
 Soc. Math. France, Paris, 1997.
3) I. Shestakov, U. Umirbaev, The tame and the wild automorphisms of
polynomial rings in three variables, J. Amer. Math. Soc., 2004, 17(1):
197-227.

books
1) A. van den Essen, Polynomial automorphisms and the Jacobian
Conjecture: Progress in Mathematics 190, Basel, Boston, Berlin:
Birkhauser, 2000.
2) A. Mikhalev, V. Shpilrain, J. Yu, Combinatorial methods: Free
groups, polynomials, and free algebras, CMS Books in Mathematics 19,
Springer-Verlag, New York, 2004.
3) Affine algebraic geometry, Edited by Takayuki Hibi, Osaka
University Press, Osaka, 2007.

Time: 2010 Oct 8 Friday, 3:10pm-4:10pm

报告人: 许权
题目: Artin reciprocity law
摘要: In classical class field theory, there are two foundamental
theorems,i.e Artin reciprocity law and Existence theorem.
   In this lecture, I will try to introduce modulus and generalized
ideal class group in order to get Kronecker -weber theorem. Also,I
give some details and examples to explain them.

Time: 2010 Oct 8 Friday,4:20pm-5:20pm
地点：数学科学学院210教室

转载本文请联系原作者获取授权，同时请注明本文来自数论研究科学网博客。
链接地址：https://blog.sciencenet.cn/blog-378289-373342.html

上一篇：Cohomology of (phi, Gamma)-modules and applications
下一篇：10,000 years of mathematics in pictures