Past Seminars- Conference

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  • David Grant
    Sat Nov 7, 2009
    10:00 am
    Serre famously proved that for elliptic curves $E$ over number fields $k$ without complex multiplication, the galois group $H$ of the field generated over $k$ by all the torsion points $E_{\text{tor}}$ of $E$ is a subgroup of finite index in $G=\displaystyle\lim_{\leftarrow\atop n} \text{GL}_2(\Bbb Z/n\Bbb Z)$. When $k=\Bbb Q$, the smallest the...
  • Sat Nov 7, 2009
    9:30 am
    Southern California Analysis and PDE Conference Day 1
  • Cristian Popescu
    Sat Oct 25, 2008
    4:00 pm
    We will discuss our recent proof (joint work with C. Greither) of a conjecture linking $\ell$-adic realizations of $1$-motives and special values of equivariant $L$-functions in characteristic $p$, refining earlier results of Deligne and Tate. As a consequence, we will give proofs (in the characteristic $p$ setting) of various central classical...
  • Jeff Achter
    Sat Oct 25, 2008
    2:30 pm
    Let E be an elliptic curve over an algebraically closed field k of characteristic p>0. Then the physical p-torsion E[p](k) is either trivial, and E is called supersingular, or E[p](k) is a group of order p. More generally, if X/k is an abelian variety of dimension g, then X[p](k) is isomorphic to (Z/p)^f for some number f, called the p-rank...
  • Jordan Ellenberg
    Sat Oct 25, 2008
    11:30 am
    A Hurwitz space H_{G,n} is an algebraic variety parametrizing branched covers of the projective line with some fixed finite Galois group G. We will prove that, under some hypotheses on G, the rational i'th homology of the Hurwitz spaces stabilizes when the number of branch points is sufficiently large compared to i. This purely topological...
  • Sat Oct 25, 2008
    10:00 am
    Southern California Number Theory Day, 10:00-5:00
  • Brian Conrad
    Sat Oct 25, 2008
    10:00 am
    Generalized ideal class groups can be described adelically in terms of a coset space for the group GL1, and this in turn leads to a notion of "class number" (as the size of a certain set, if finite) for an arbitrary affine algebraic group over a global field. Related to this is the notion of the "Tate-Shafarevich set" of an algebraic group, which...