Following a formula found in the paper of Avramov, Iyengar, Lipman, and Nayak
(2010) and ideas of Neeman and Khusyairi, we indicate that Grothendieck duality
for finite tor-amplitude maps can be developed from scratch via the formula
f!:=Ξ΄βΟ1Γβfβ. Our strategy centers on the subcategory
ΞΞβ(QCoh(XΓX)) of quasicoherent sheaves on XΓX supported on the diagonal. By exclusively using this subcategory
instead of the full category QCoh(XΓX) we give systematic
categorical proofs of results in Grothendieck duality and reprove many formulas
found in Neeman (2018). We also relate some results in Grothendieck duality
with properties of the sheaf of (derived) Grothendieck differential operators.Comment: 27 page