9 citations · 13 across the 5 of their papers we have counts for
5 papers
The root closure of a ring of mixed characteristic
Paul C. Roberts
We define a closure operation for rings of mixed characteristic and verify that the closure is a ring. We then show that this closure produces a ring with good properties with resp…
An algebraic proof of the commutativity of the intersection with divisors
Paul Roberts, Sandra Spiroff
We present a purely algebraic proof of the commutativity of the operation defined by intersection with divisors on the Chow group of a local Noetherian domain.
Annihilators of Local Cohomology in Characteristic Zero
Paul Roberts, Anurag K. Singh, V. Srinivas
This paper discusses the problem of whether it is possible to annihilate elements of local cohomology modules by elements of arbitrarily small order under a fixed valuation. We fir…
Cycles and Commutative Algebra
Paul C. Roberts
We describe several applications of the theory of cycles to questions in Commutative Algebra. The main topic is the use of the theory of local Chern characters to answer some quest…
Heitmann's proof of the direct summand conjecture in dimension 3
Paul Roberts
We discuss Ray Heitmann's recent proof of the Direct Summand Conjecture in dimension 3 in mixed characteristic. This paper contains a discussion of his methods, a proof of the theo…