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比利时vs摩洛哥足彩 ,
university of california san diego

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math 209 - number theory

james barrett

king's college london

dirichlet l-functions at strictly positive integers and fitting invariants of k-groups

abstract:

for k a c.m. abelian extension of a totally real base-field k with galois group g, solomon has recently constructed for each prime p a z p[g] ideal of q p[g] related to values of dirichlet l-functions at s=1 and conjectured that this ideal is contained within z p[g]. jones has subsequently shown that for each odd p the equivariant tamagawa number conjecture (or etnc) implies that solomon's ideal should actually be contained within the fitting ideal of the class-group of o k. i shall explain how to define analogous ideals related to values of dirichlet l-functions at integers r strictly greater than 1 and provide a sketch of the techniques used to show that the etnc relates these `higher solomon ideals' to the fitting ideals of certain natural cohomology groups (and thus, when the quillen-lichtenbaum conjecture is valid, to fitting ideals of quillen k-groups of o k). in particular, for certain choices of k/k and r these results are unconditional as the relevant cases of the etnc and quillen-lichtenbaum conjecture are known to be valid.

host: cristian popescu

february 22, 2007

1:00 pm

ap&m 7321

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