比利时vs摩洛哥足彩
,
university of california san diego
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math 209 - number theory
cristian popescu
ucsd
1-motives, etale cohomology and equivariant iwasawa theory
abstract:
the classical conjectures of gross and brumer-stark seem to describe two completely unrelated properties of special values of galois equivariant global l-functions. in this talk, we will develop a general equivariant main conjecture in iwasawa theory which captures the brumer-stark and gross phenomena simultaneously and works equally well in characteristics $0$ and p. the characteristic p side of the theory draws its main ideas from deligne\'s construction of $1-motives$ associated to smooth, projective curves over finite fields. the characteristic $0$ side of the theory is based on our new construction of number field analogues of the l-adic realizations (i.e. l-adic etale cohomology groups) of deligne\'s $1-motives$ and is deeply rooted in earlier work of tate and ritter - weiss on the theory of multiplicative galois module structure. time permitting, we will also provide evidence in support of this new equivariant iwasawa theoretic statement and discuss its links to l-adic refinements of integral rubin - stark - type conjectures on special values of global l-functions.
host:
november 20, 2003
1:00 pm
ap&m 7321
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