An Abelian variety is a geometrically complete group scheme over a field. It must be projective, smooth, and commutative. An algebraic group is also a complete algebraic variety.
Because she already had a certain foundation, Wu Tong solved the Tate conjecture before Faltings and promoted the idea and calculation method of using Abelian clusters, and found inspiration for the way forward. Although these inspirations cannot allow her to solve the BSD conjecture immediately, Wu Tong can be sure that if she continues along this path, she can reach the end. This is more important than anything else!
Of course, this was undoubtedly the most difficult part, but Wu Tong still wanted to try and see if he could complete it.
It can be said that she did not start from scratch this time, but made a pleasant breakthrough in the area of optimization and enhancement, which she is good at.
The energy consumption of the enlightenment state is very high and the time is limited. When Wu Tong found the direction of the enlightenment stele, he almost ran out of energy to continue and was forced to automatically cut off the enlightenment state.
Of course, this didn't really affect Wu Tong much. By then, it was already July. Wu Tong spent two days saving her preliminary paper on the ABC conjecture and then continued to work on the BSD conjecture. For her, the breakthrough in the ABC conjecture was no longer the most important issue; her new goal, the BSD conjecture, was her undivided attention.
Having found a clear solution, Wu Tong didn't have an overwhelming desire for the Enlightenment Space. She always trusted what she had learned. It wasn't that Wu Tong was arrogant and thought she didn't need help; everyone didn't want to take shortcuts. Rather, she understood that help needed to be based on a solid foundation in order to achieve a positive effect, and couldn't rely on the Enlightenment State.
Wu Tong completed the final proof on the right path at an almost mad speed.
Substituting this into Modal's theorem and BSD conjecture, the proof is correct.