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In this paper we give a short introduction to the local uniformization problem. This follows a similar line as the one presented by the second author in his talk at ALANT 3. We also discuss our paper on the reduction of local uniformization to the rank one case. In that paper, we prove that in order to obtain local uniformization for valuations centered at objects of a subcategory of the category of noetherian integral domains, it is enough to prove it for rank one valuations centered at objects of the same category. We also announce an extension of this work which was partially developed during ALANT 3. This extension says that the reduction mentioned above also works for noetherian rings with zero divisors (including the case of non-reduced rings).
Josnei Novacoski, and Mark Spivakovsky. "On the local uniformization problem." Banach Center Publications 108.1 (2016): 231-238. <http://eudml.org/doc/286155>.
@article{JosneiNovacoski2016, abstract = {In this paper we give a short introduction to the local uniformization problem. This follows a similar line as the one presented by the second author in his talk at ALANT 3. We also discuss our paper on the reduction of local uniformization to the rank one case. In that paper, we prove that in order to obtain local uniformization for valuations centered at objects of a subcategory of the category of noetherian integral domains, it is enough to prove it for rank one valuations centered at objects of the same category. We also announce an extension of this work which was partially developed during ALANT 3. This extension says that the reduction mentioned above also works for noetherian rings with zero divisors (including the case of non-reduced rings).}, author = {Josnei Novacoski, Mark Spivakovsky}, journal = {Banach Center Publications}, language = {eng}, number = {1}, pages = {231-238}, title = {On the local uniformization problem}, url = {http://eudml.org/doc/286155}, volume = {108}, year = {2016}, }
TY - JOUR AU - Josnei Novacoski AU - Mark Spivakovsky TI - On the local uniformization problem JO - Banach Center Publications PY - 2016 VL - 108 IS - 1 SP - 231 EP - 238 AB - In this paper we give a short introduction to the local uniformization problem. This follows a similar line as the one presented by the second author in his talk at ALANT 3. We also discuss our paper on the reduction of local uniformization to the rank one case. In that paper, we prove that in order to obtain local uniformization for valuations centered at objects of a subcategory of the category of noetherian integral domains, it is enough to prove it for rank one valuations centered at objects of the same category. We also announce an extension of this work which was partially developed during ALANT 3. This extension says that the reduction mentioned above also works for noetherian rings with zero divisors (including the case of non-reduced rings). LA - eng UR - http://eudml.org/doc/286155 ER -