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p進ホッジ理論（ホッジ＝テイト予想の解決、ド・ラーム予想の解決、クリスタリンヌ予想の解決、半安定予想の別証明）と非可換p進ホッジ理論の構築、 {Z} 上におけるトロイダルコンパクト化の構成、ディオファントス近似論におけるファルティングスの定理 (Product Theorem)、クリスタリンヌ層の構成、almost etale拡大の理論、数論的リーマン・ロッホの定理、リジッド幾何学の代数スタックへの応用などの業績がある。
プリンストン大学教授時代、Ph.D.課程に在籍していた望月新一の指導教員をしていた。

https://en.wikipedia.org/wiki/Gerd_Faltings
Gerd Faltings
References
1. Castelvecchi, Davide (7 October 2015). "The biggest mystery in mathematics: Shinichi Mochizuki and the impenetrable proof". Nature. 526 (7572): 178?181.
https://www.nature.com/articles/526178a
The reason is that Mochizuki's work is so far removed from anything that had gone before. He is attempting to reform mathematics from the ground up, starting from its foundations in the theory of sets (familiar to many as Venn diagrams). And most mathematicians have been reluctant to invest the time necessary to understand the work because they see no clear reward: it is not obvious how the theoretical machinery that Mochizuki has invented could be used to do calculations. “I tried to read some of them and then, at some stage, I gave up. I don't understand what he's doing,” says Faltings.

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