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Conference on Stark's Conjectures and related topics August 5-9, 2002 Johns Hopkins University, Department of Mathematics Stark’s Conjecture has over the course of the last twenty years been seen to be one of the deepest unsolved problems in number theory. In the last few years there has been a surge in research activity dedicated towards obtaining further explicit evidence for this conjecture, and in formulating and investigating interesting variants, refinements or generalizations of it. By bringing together the researchers from these different strands, we expect to improve understanding of the links between them. In turn, the better understanding of these links should provide an ideal platform from which research into all aspects of Stark's Conjecture will benefit significantly. Topics
to be covered will include the following. Explicit
refinements of Stark’s Conjecture in the abelian case:
a)
The Brumer-Stark Conjecture. b)
The Conjectures of Gross and of Tate (concerning the values of Dirichlet
L-functions modulo augmentation ideal filtrations). c)
The Conjectures of Rubin and of Popescu (concerning the values of higher
derivatives of Dirichlet L-functions). d)
The connection to Euler systems, special units, Gras-type Conjectures. p-adic
analogues:
a)
The Conjecture of Gross (at s = 0) b)
The Conjecture of Serre (at s = 1) and Solomon’s p-adic analogue of the conjecture of Rubin.
Special
values conjectures for Artin L-functions at integers other than 0 or 1:
a)
The Conjectures of Gross and of Lichtenbaum. b)
The Conjecture of Coates and Sinnott. The
Equivariant Tamagawa Number Conjecture of Burns-Flach:
a)
Connections to the seminal work of Bloch and Kato, and of Fontaine and Perrin-Riou,
and consequences thereof. b) Equivariant Iwasawa Theory The
connection to Galois module theory:
The
conjectures of Chinburg and the Lifted Root Number Conjecture of Gruenberg-Ritter-Weiss.
Computational
Aspects: a)
Computational techniques and results concerning verification of Stark's
Conjecture, its variants and generalizations. b)
Construction of class fields, Hilbert’s 12th problem.
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