论文标题
张量产品和傅立叶变换的Hilbert-Kunz密度函数
Hilbert-Kunz Density function of tensor product and Fourier transformation
论文作者
论文摘要
对于标准的级环$ r $的尺寸$ \ geq 2 $，在一个完美的特征$ p> 0 $和同质的理想$ i $的完美领域，相对于$ i $，$ r $的HK密度函数相对于$ i $，是一个紧凑的连续函数$ f_ {r，i} \ mbox {hk}乘数$ e_ {hk}（r，i）$。 在这里，我们回答了V. trivedi的问题，内容涉及标准分级环的张量产物的Hilbert-Kunz密度函数，并表明这是因子环的Hilbert-Kunz密度函数的卷积。使用傅立叶变换，作为推论，我们获得了环的张量产物的\ mbox {hk}多重性，是因子环的HK多样性的产物。我们计算\ mbox {hk}的傅立叶变换的射击曲线密度函数。
For a standard graded ring $R$ of dimension $\geq 2$ over a perfect field of characteristic $p>0$ and a homogeneous ideal $I$ of finite colength, the HK density function of $R$ with respect to $I$ is a compactly supported continuous function $f_{R, I}:[0, \infty)\longto [0, \infty)$, whose integration yields the \mbox{HK} multiplicity $e_{HK}(R, I)$. Here we answer a question of V. Trivedi about the Hilbert-Kunz density function of the tensor product of standard graded rings and show that it is the convolution of the Hilbert-Kunz density function of the factor rings. Using Fourier transform, as a corollary we get \mbox{HK} multiplicity of the tensor product of rings is product of the HK multiplicity of the factor rings. We compute the Fourier transform of the \mbox{HK} density function of a projective curve.
