Tamagawa Number of Elliptic Curves over \$\mathbb{Q}\$ - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-25T03:56:41Z http://mathoverflow.net/feeds/question/96542 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/96542/tamagawa-number-of-elliptic-curves-over-mathbbq Tamagawa Number of Elliptic Curves over \$\mathbb{Q}\$ Eugene 2012-05-10T06:25:25Z 2012-05-10T07:30:35Z <p>I am currently reading a paper by De Weger and one theorem in it proves a bound for the Tamagawa number of any elliptic curve defined over \$\mathbb{Q}\$. </p> <p>I was wondering if anyone has any good references/texts that provide an exposition on the Tamagawa number of an elliptic curve as I was unable to find one in the Arithmetic of Elliptic Curves. </p> <p>I know the definition of the Tamagawa number from this reference, but not really much more than that (http://math.uci.edu/~asilverb/connectionstalk.pdf).</p> <p>EDIT: I am looking for something a little more in depth than the intuition behind the definition. For instance useful recent applications of Tamagawa numbers or what is known about Tamagawa numbers for elliptic curves over \$\mathbb{Q}\$.</p> http://mathoverflow.net/questions/96542/tamagawa-number-of-elliptic-curves-over-mathbbq/96543#96543 Answer by Srilakshmi for Tamagawa Number of Elliptic Curves over \$\mathbb{Q}\$ Srilakshmi 2012-05-10T06:35:48Z 2012-05-10T06:45:27Z <p>Look at <a href="http://mathoverflow.net/questions/71044/intuition-behind-the-tamagawa-number" rel="nofollow">http://mathoverflow.net/questions/71044/intuition-behind-the-tamagawa-number</a> : Tate's article in Antwerp IV (Springer Lecture Notes in Mathematics 476), Modular Functions of One Variable IV.</p> http://mathoverflow.net/questions/96542/tamagawa-number-of-elliptic-curves-over-mathbbq/96547#96547 Answer by Marc Palm for Tamagawa Number of Elliptic Curves over \$\mathbb{Q}\$ Marc Palm 2012-05-10T07:30:35Z 2012-05-10T07:30:35Z <p>I think I would start with Weil "Adeles and algebraic groups", but if you are looking for something more specifically associated to elliptic curves, maybe this survey of Guido Kings: <a href="http://epub.uni-regensburg.de/13613/1/MP6.pdf" rel="nofollow">http://epub.uni-regensburg.de/13613/1/MP6.pdf</a> is a good starting point to see the connection between the Equivariant Tamagawa Number conjecture and the BSD conjecture, and consider the references therein.</p> <p>And here is anothor one of M.Flach: <a href="http://www.math.caltech.edu/papers/baltimore-final.pdf" rel="nofollow">http://www.math.caltech.edu/papers/baltimore-final.pdf</a></p>