https://www.foxbusiness.com/politics/tennessee-sues-blackrock-first-of-its-kind-esg-lawsuit

Bottom line from my admittedly unedumacated POV the fiduciary violations are in regard to failing to focus on the financial best-interests of clients as top priority. Applying ESG-driven modifications in portfolios, such as excluding fossil fuel companies because of concerns about AGW  - without informing clients of this policy may be a violation. 

There have also apparently been some duplicitous communications to clients and client-companies about policies which misleading them purposefully, in order to serve the needs of political zealots within Black Rock administrative levels and affiliated entities in control of funds - another violation. 

Mebbe not all of the courts can be bought off by greenhead ACF* multinationals trying to align with government power. 

*ACF = Anti-Conservative Fanatics (i.e., self-described "liberal" or "progressive" 'Crats)