A p-adic approach to rational points on curves
Name
S0273-0979-2020-01707-6.pdf
Description
Published version
Size
254.76 KB
Format
Adobe PDF
Checksum (MD5)
e02ec1c666e7d48db4ca751423fdc434
Author(s)
Poonen, Bjorn
Date Issued
2020
Journal
Bulletin of the American Mathematical Society
Publisher
American Mathematical Society (AMS)
Version
Final published version
Abstract
© 2021. American Mathematical Society. In 1922 Mordell conjectured the striking statement that, for a polynomial equation f(x, y) = 0, if the topology of the set of complex number solutions is complicated enough, then the set of rational number solutions is finite. This was proved by Faltings in 1983 and again by a different method by Vojta in 1991. But neither proof provided a way to provably find all the rational solutions, so the search for other proofs has continued. Recently, Lawrence and Venkatesh found a third proof, relying on variation in families of p-adic Galois representations; this is the subject of the present exposition.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1090/BULL/1707
