31 citations · 68 across the 17 of their papers we have counts for
22 papers
Bertini's theorem for -rational -pure singularities
Alessandro De Stefani, Thomas Polstra, Austyn Simpson
Let be an algebraically closed field of characteristic , and let be a quasi-projective variety that is -rational and -pure. We prove that…
-injectivity does not imply -fullness in normal domains
Alessandro De Stefani, Thomas Polstra, Austyn Simpson
We construct examples of noetherian three-dimensional local geometrically normal domains of prime characteristic which are -injective but not -full. Along the way, we find ex…
Strong -regularity and the Uniform Symbolic Topology Property
Thomas Polstra
We investigate the containment problem of symbolic and ordinary powers of ideals in a commutative Noetherian domain . Let be a normal domain of prime characteristic th…
Zariski-Nagata Theorems for Singularities and the Uniform Izumi-Rees Property
Thomas Polstra
We introduce and explore the Uniform Izumi-Rees Property in Noetherian rings with applications to multiplicity theory and containment relationships among symbolic powers of ideals.…
On -pure inversion of adjunction
Thomas Polstra, Austyn Simpson, Kevin Tucker
We analyze adjunction and inversion of adjunction for the -purity of divisor pairs in characteristic . In this vein, we give a complete answer for principal divisors unde…
Primary Decompositions of Regular Sequences
Thomas Polstra
Let be a Noetherian ring and a permutable regular sequence of elements in . Then there exists a finite set of primes and natural number so that for…