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SUMMARY:Niven T. Achenjang (MIT)
DTSTART:20240229T210000Z
DTEND:20240229T223000Z
DTSTAMP:20260422T172132Z
UID:STAGE/100
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/STAGE/100/">
 The Mordell-Weil theorem and Chabauty's theorem</a>\nby Niven T. Achenjang
  (MIT) as part of STAGE\n\nLecture held in Room 2-131 in the MIT Simons Bu
 ilding.\n\nAbstract\nChapter 4 and Section 5.1 of Serre\, Lectures on the 
 Mordell-Weil theorem.\n\nThis talk will be split into two parts. In the fi
 rst part\, we will discuss the Mordell-Weil Theorem\, which states that th
 e abelian group of rational points on an abelian variety $A$ defined over 
 a global field $K$ is finitely generated. We will show that this theorem f
 ollows from some classical finiteness results in algebraic number theory a
 long with the theory of heights built up in previous talks. Time permittin
 g\, we will conclude the first part by proving a theorem of Neron which gi
 ves an asymptotic count for the number of points of bounded height on an a
 belian variety of rank $\\rho$. In the second part\, we will turn our atte
 ntion towards curves of genus $g\\ge2$. For such curves $C/K$\, we will pr
 ove Chabauty's Theorem that $C(K)$ is finite if $\\operatorname{rank}\\ope
 ratorname{Jac}(C)(K) < g$ (finiteness of $C(K)$ is now known even when $C$
 's Jacobian has large rank).\n
LOCATION:https://researchseminars.org/talk/STAGE/100/
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