Proves logarithmic extension of one-forms on strongly F-regular singularities and on 3D klt singularities in char p>41 by reducing via Cartier operators to the 2D klt case with imperfect residue fields.
Hacon, and James McKernan
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A combinatorial criterion decides finite generation of valuation semigroups on smooth toric surfaces for non-toric maximal-rank valuations, plus a lattice polytope where none from one-parameter subgroups at a non-toric point are finitely generated.
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Extending one-forms on $F$-regular singularities
Proves logarithmic extension of one-forms on strongly F-regular singularities and on 3D klt singularities in char p>41 by reducing via Cartier operators to the 2D klt case with imperfect residue fields.
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On the finite generation of valuation semigroups on toric surfaces
A combinatorial criterion decides finite generation of valuation semigroups on smooth toric surfaces for non-toric maximal-rank valuations, plus a lattice polytope where none from one-parameter subgroups at a non-toric point are finitely generated.