Kavli Affiliate: Tomoyuki Abe
| First 5 Authors: Tomoyuki Abe, Christopher Lazda, , ,
| Summary:
For any separated, taut, locally of $^+$weakly finite type morphism
$f:Xrightarrow Y$ between finite dimensional, analytic adic spaces, we
construct the higher direct images with compact support
$mathbf{R}^qf_!mathscr{F}$ of any abelian sheaf $mathscr{F}$ on $X$. The
basic approach follows that of Huber in the case of ‘etale sheaves, and rests
upon his theory of universal compactifications of adic spaces. We show that
these proper pushforwards satisfy all the expected formal properties, and
construct the trace map and duality pairing for any (separated, taut) smooth
morphism of adic spaces, without assuming partial properness.
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