Group, Lie and Number Theory Date:  Monday, January 14, 2013 Location:  4096 East Hall (3:00 PM to 5:00 PM) Title:  Pairs of p-adic analogues of the conjectures of Birch and Swinnerton-Dyer Abstract:   The classical conjectures of Birch and Swinnerton-Dyer relate the behavior of the Hasse-Weil L-function of an elliptic curve to its Q-rational points. For primes of good reduction, there are p-adic analogues of these conjectures due to Mazur, Tate, and Teitelbaum (ordinary case), and due to Bernardi and Perrin-Riou (supersingular case). In this talk, we would like to present a pair of convenient p-adic L-functions that can be used to rewrite (and thus unite) their conjectures. These p-adic L-functions provide us with growth formulas for the Tate-Shafarevich group along the cyclotomic Z_p extension. If time permits, there will be a picture describing the analogous behavior for weight two modular forms. Speaker:  Florian Sprung Institution:  Brown University Event Organizer:      mityab@umich.edu   Edit this event (login required). Add new event (login required). For access requests and instructions, contact math-webmaster@umich.edu Back to previous page Back to UM Math seminars/events page.