Extension Data of Global Families of Mixed Hodge Structures - Applications to Shafarevich Conjecture

Explore a 33-minute conference talk by Mark Green from UCLA on the extension data of global families of mixed Hodge structures and their applications to the Shafarevich Conjecture. Delve into the structure of mixed Hodge structures, examining how their graded pieces form Hodge structures with variable extension data between them. Learn about the levels of extension data, with level 1 occurring between adjacent graded pieces and level 2 involving a degree skip of two. Discover how global families of mixed Hodge structures can be characterized by monodromy on graded pieces and extension data of levels 1 and 2, capturing all but discrete invariants. Understand how this approach leads to an alternative proof of the nilpotent case of Shafarevich's Conjecture, providing valuable insights into algebraic geometry and Hodge theory.