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\vspace*{0.6875cm} {\bf A counterexample to Rosick\'y's conjecture}
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{\sc Silvana Bazzoni}\\
Universit\'a di Padova

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\noindent
 We show that if $k$ is an uncountable field, the $\lambda$-pure global dimension of $k[x,y]$ as well as of the Kronecker algebra over $k$ is greater than one for every regular cardinal $\lambda$. This answer in negative a problem
of Rosick\'y. As a consequence, the $\lambda$-Brown-Adams representability fails for the derived categories of these rings.

This is joint work with Jan \v S\v tov\' \i\v cek.


 
 

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