WorkshopsIwasawa theory of modular forms at nonordinary primes
129
reads
The Iwasawa theory of modular forms concerns the p-adic interpolation of their arithmetic data, e.g. their p-adic L-functions. Thanks to the work of many mathematicians, we have a detailed understanding of many parts of this picture. But Galois-theoretic aspects in the non-ordinary case have been particularly resistant to analysis, and understanding this case is a major goal of current reasearch. We will explain a new method for bringing most nonordinary primes onto an equal footing with the ordinary ones, in such a way that much of our intuition generalizes. We make use of recent improvements in p-adic Hodge theory and Galois cohomology.
reads
Jonathan Pottharst
2010-07-16
10:40:00 - 12:00:00
101 , Mathematics Research Center Building (ori. New Math. Bldg.)
The Iwasawa theory of modular forms concerns the p-adic interpolation of their arithmetic data, e.g. their p-adic L-functions. Thanks to the work of many mathematicians, we have a detailed understanding of many parts of this picture. But Galois-theoretic aspects in the non-ordinary case have been particularly resistant to analysis, and understanding this case is a major goal of current reasearch. We will explain a new method for bringing most nonordinary primes onto an equal footing with the ordinary ones, in such a way that much of our intuition generalizes. We make use of recent improvements in p-adic Hodge theory and Galois cohomology.