@article {487, title = {The motivic Thom-Sebastiani theorem for regular and formal functions}, journal = {Journal f{\"u}r die reine und angewandte Mathematik}, volume = {735}, year = {2018}, month = {02/2018}, pages = {175-198}, chapter = {175}, abstract = {Thanks to the work of Hrushovski and Loeser on motivic Milnor fibers, we give a model-theoretic proof for the motivic Thom{\textendash}Sebastiani theorem in the case of regular functions. Moreover, slightly extending Hrushovski{\textendash}Loeser{\textquoteright}s construction adjusted to Sebag, Loeser and Nicaise{\textquoteright}s motivic integration for formal schemes and rigid varieties, we formulate and prove an analogous result for formal functions. The latter is meaningful as it has been a crucial element of constructing Kontsevich{\textendash}Soibelman{\textquoteright}s theory of motivic Donaldson{\textendash}Thomas invariants.}, doi = {10.1515/crelle-2015-0022}, url = {http://www.degruyter.com/view/j/crll.ahead-of-print/crelle-2015-0022/crelle-2015-0022.xml?format=INT}, author = {L{\^e}, Quy Thuong} }