Commutative algebra 50: Hensel's lemma

แชร์
ฝัง
  • เผยแพร่เมื่อ 21 ม.ค. 2025

ความคิดเห็น • 11

  • @migarsormrapophis2755
    @migarsormrapophis2755 4 ปีที่แล้ว +1

    yee

  • @f5673-t1h
    @f5673-t1h 4 ปีที่แล้ว +1

    I always like pointing out that Hensel's lemma is just the analogue of Newton's method for Qp.

    • @Ray25689
      @Ray25689 4 ปีที่แล้ว

      You mean the proof?

    • @f5673-t1h
      @f5673-t1h 4 ปีที่แล้ว +1

      @@Ray25689 sometimes in textbooks they don't tell you this connection, so it doesn't seem like an intuitive result. So some people could know about the lemma, but don't know it's just Newton's method.

    • @Ray25689
      @Ray25689 4 ปีที่แล้ว

      @@f5673-t1h thats true
      If you first read it, it looks way more abstract than it actually is, IMO
      Depends on the formulation tho

    • @theflaggeddragon9472
      @theflaggeddragon9472 4 ปีที่แล้ว

      Which is also "formally" equivalent to the implicit function theorem. I haven't seen anything deep said about these interpretations though, perhaps they help some people gain some intuition. Personally, I tend to think of each of these results on their own terms.

    • @theflaggeddragon9472
      @theflaggeddragon9472 4 ปีที่แล้ว

      Here's a neat discussions on MSE: math.stackexchange.com/questions/48419/hensels-lemma-and-implicit-function-theorem