 \titleofpresentation{Variants of the Cycle Class Map}
 \presenter{James D. Lewis}


 The celebrated Hodge conjecture
in its classical form, is a statement about the
image of a particular cycle class map from an algebraic
cycle group on a nonsingular complex projective variety
to singular cohomology. We give a precise
statement of this conjecture from an algebraic
point of view. We then discuss a 
variant of this conjecture, called the Hodge-Deligne
conjecture. Next, and motivated in
part by constructions in algebraic K-theory, we consider
twisted variants of this cycle class map construction,
and explain the advantages of this construction over
the original cycle class map.

 \presenteraddress{Department of Mathematics, University of Alberta,\\
Edmonton, Alberta T6G~2G1, Canada}

\email{lewisjd@ualberta.ca}

\web{www.math.ualberta.ca/Lewis_JD.html}
 

