DynaLite Graduate Student Seminar Carl Olimb p-adic Numbers Department of Mathematical Sciences

DynaLite Graduate Student Seminar
p-adic Numbers
Carl Olimb
Department of Mathematical Sciences
Montana State University
Monday, March 27, 4:10 – 5:00 pm
2–244 Hurst Conference Room
Over the last century, p-adic numbers have come to play a central role in modern
number theory. The analogy between the fields Qp and R is easily understood and
provides helpful information when dealing with a variety of problems. In this talk I
will investigate the construction of Qp by completing Q for all of its nontrivial absolute
values. Also, the similarities between the two fields Qp and R will be discussed. In
particular, work will be done with Hensel’s lemma and the local/global properties of
Hasse-Minkowski Theorem for three indeterminates.