14 citations · 85 across the 21 of their papers we have counts for
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math.AC2020★ 3 cited
Excellence, F-singularities, and solidity
Rankeya Datta, Takumi Murayama, Karen E. Smith
An -algebra is -solid if there exists a nonzero -linear map . In characteristic , the study of -singularities such as Frobenius splittings impli…
math.AG2020★ 11 cited
A uniform treatment of Grothendieck's localization problem
Takumi Murayama
Let be a proper flat morphism of locally noetherian schemes. Then, the locus in over which is smooth is stable under generization. We prove that under sui…
math.AC2020★ 4 cited
Tate algebras and Frobenius non-splitting of excellent regular rings
Rankeya Datta, Takumi Murayama
An excellent ring of prime characteristic for which the Frobenius map is pure is also Frobenius split in many commonly occurring situations in positive characteristic commutative a…