Abstract
The aim of the lectures is to present the Dieudonn$\acute{e}$ theory
over perfect fields of positive characteristic. More precisely, if
$k$ is a perfect field of characteristic $p > 0$, we will assign,
functorially, to every $p$torsion finite commutative group scheme
over $k$ a finite length module over the ring of Witt vectors,
called the Dieudonn$\acute{e}$ module, endowed with two
endomorphisms $F$ (Frobenius) and $V$ (Verschiebung) satisfying
certain identities. This assignment turns out to be an
antiequivalence of categories, from the category of finite
commutative $p$group schemes over $k$ and the category of modules
over the Dieudonn$\acute{e}$ ring $\frac{W(k)[F,V]}{(FV =VF=p)}$,
which are of finite length over the ring of Witt vectors, $W(k)$. We
can also extend this equivalence between the category of $p$torsion
commutative formal group schemes over $k$ and the category of
modules over the Dieudonn$\acute{e}$ ring of $k$, which are finitely
generated over $W(k)$. If time permits, as an application, we will
give a classification of $p$divisible groups over $k$.
Information:
Date:  Wednesday, July 22, 2009,
Monday, July 27, 2009
Wednesday, July 29, 2009
Monday, August 3, 2009
Wenesday, August 5, 2009
Monday, August 10, 2009
Wednesday, August 12, 2009
 Time:  14:0015:45 and 16:1518:00 
Place:  Niavaran Bldg., Niavaran Square, Tehran, Iran 
