Obama did not modernize the U.S. nuclear arsenal. He promised to modernize it in exchange for Republican support in the Senate to pass the New START arms control deal. But he let the nuclear enterprise fall into such disrepair that a major scandal emerged in 2013, leading to a major DOD effort to repair the enterprise after a review in 2014: https://www.gao.gov/products/GAO-19-29. He kicked the can down the road on modernization of the arsenal itself until the very tail end of his administration, so that it was up to Trump in 2017 to follow through on the promise Obama made back in 2010. All of this occurred after Obama had won the Nobel Peace Prize.