Tail dependence in the pseudo-observations of bivariate copula imply that extreme upper or lower samples move together in some way suggesting correlation between the two marginals' (variables') extreme samples.
Kurtosis on the other hand describes the fat-tails found in the extreme samples of only one non-Gaussian univariate (marginal) distribution, therefore lacking the dependence feature.
Since both concepts address extreme samples, but with tail dependence being a concept applied to bivariate data, and kurtosis applied to univariate data (therefore correlation of extreme samples does not apply to kurtosis), is there some sort of connection between copula tail dependence and univariate (or maybe multivariate) kurtosis? i.e. does high tail dependence indicate kurtosis somehow, or vice versa?