11 citations · 52 across the 18 of their papers we have counts for
8 papers · 1 filter
Hilbert-Kunz theory for nodal cubics, via sheaves
Paul Monsky
Suppose B=F[x,y,z]/h is the homogeneous coordinate ring of a characteristic p degree 3 irreducible plane curve C with a node. Let J be a homogeneous (x,y,z)-primary ideal and n ->…
The limit as p -> infinity of the Hilbert-Kunz multiplicity of sum(x_i^(d_i))
Ira M. Gessel, Paul Monsky
Let p be a prime. The Hilbert-Kunz multiplicity, mu, of the element sum(x_i^(d_i)) of (Z/p)[x_1,..., x_s] depends on p in a complicated way. We calculate the limit of mu as p -> in…
Transcendence of some Hilbert-Kunz multiplicities (modulo a conjecture)
Paul Monsky
Suppose that h in F[x,y,z], char F=2, defines a nodal cubic. In earlier papers we made a precise conjecture as to the Hilbert-Kunz functions attached to the powers of h. Assuming t…
Algebraicity of some Hilbert-Kunz multiplicities (modulo a conjecture)
Paul Monsky
Let F be a finite field of characteristic 2 and h be the element x^3+y^3+xyz of F[[x,y,z]]. In an earlier paper we made a precise conjecture as to the values of the colengths of th…
Tight closure's failure to localize - a self-contained exposition
Paul Monsky
We give a treatment of the Brenner-Monsky example based on polynomial algebra and linear algebra. No prior knowledge of tight closure theory, Hilbert-Kunz theory, algebraic geometr…
Tight closure does not commute with localization
Holger Brenner, Paul Monsky
We give an example showing that tight closure does not commute with localization.