Mathematical Sciences: Problems Related to Lech's Conjectureand Some Questions on Divisor Class Groups

本报告将涉及两个方面 research.首先，将考虑以下问题： 关于《易经》的一个问题， 局部忠实平坦态射下的Hilbert函数 诺特环在第二种情况下，首席研究员 将研究除数类群的稳定性 其中R是局部正规优良Henselian环。 本研究涉及的几何性质 在代数几何中出现的交换环。之一 要考虑的问题是莱赫的一个猜想， 二十五年来一直没有解决。

There are two areas which will be addressed in this research. In the first, problems will be considered which are related to a conjecture by Lech concerning the behavior of the Hilbert function under faithfully flat morphisms of local noetherian rings. In the second, the principal investigator will study stability properties of the divisor class group CL(R) where R is a local normal excellent henselian ring. This research is concerned with the geometric properties of commutative rings which arise in algebraic geometry. One of the problems to be considered is a conjecture by Lech which has been unsolved for twenty-five years.