Workshop on Special Cycles and Related Topics

Abstract: : Let $g$:$X \rightarrow S$ be a smooth proper family over algebraic varieties over a number field $K$. Consider the statement $W(g,p)$: the weight-monodromy conjectures hold for all fibres of g defined over a finite extension $L/Q_p$. We sketch a proof of the following statement: there exists a constant $c$ depending on $g$ such that $W(g,p)$ holds when $p > c$.