This paper presents a method for many-to-one voice conversion using phonetic posteriorgrams (PPGs) based on an adversarial training of deep neural networks (DNNs). A conventional method for many-to-one VC can learn a mapping function from input acoustic features to target acoustic features through separately trained DNN-based speech recognition and synthesis models. However, 1) the differences among speakers observed in PPGs and 2) an over-smoothing effect of generated acoustic features degrade the converted speech quality. Our method performs a domain-adversarial training of the recognition model for reducing the PPG differences. In addition, it incorporates a generative adversarial network into the training of the synthesis model for alleviating the over-smoothing effect. Unlike the conventional method, ours jointly trains the recognition and synthesis models so that they are optimized for many-to-one VC. Experimental evaluation demonstrates that the proposed method significantly improves the converted speech quality compared with conventional VC methods.