Lifting and restricting
t-structures
We explore the interplay of
t-structures in the bounded derived category
of finitely generated modules
and the unbounded derived category of all
modules over a noetherian ring
A. More precisely, we show that every
intermediate t-structure in
D^b(A) lifts to a compactly generated
t-structure in D(A), by
closing the respective classes under directed
homotopy colimits. Conversely,
we provide necessary and sufficient
conditions for a compactly
generated t-structure in D(A) to restrict to
an intermediate t-structure in
D^b(A). Finally, we consider the special
case of HRS-t-structures and
discuss applications to silting theory.
This talk is based on joint work
with Alexandra Zvonareva.