学术报告（姚宁远 2024.3.11）
On Algebraicity Conjecture and p-adic semialgebraic groups
摘要：Boris Zilber conjectured that any simple group of finite Morley rank is isomorphic to an algebraic group over an algebraically closed field, which was formulated in Cherlin's paper, without the finiteness of rank assumption. The conjecture now was known as the Cherlin-Zilber Conjecture or Algebraicity Conjecture. The Algebraicity Conjecture is intuitively stated as "groups definable in some ``tame'' structures are essentially algebraic groups".
In the p-adic context, definable groups are precisely semialgebraic groups. In this talk we will present several results regarding algebraicity of groups definable over the field of p-adic numbers. Our recent results indicate that: (1) Every p-aidc definable/semialgebraic group is an extension of an open subgroup of a p-adic algebraic group by a finite group. (2) Conversely, every open subgroup of a commutative (or reductive) p-adic algebraic group is definable/semialgebraic.
