4 citations · 7 across the 8 of their papers we have counts for
8 papers
On the arithmetic of tight closure
Holger Brenner, Mordechai Katzman
We provide a negative answer to an old question in tight closure theory by showing that the containment x^3y^3 \in (x^4,y^4,z^4)^* in K[x,y,z]/(x^7+y^7-z^7) holds for infinitely ma…
On a problem of Miyaoka
Holger Brenner
We give an example of a vector bundle E on a relative curve C --> Spec Z such that the restriction to the generic fiber in characteristic zero is semistable but such that the restr…
Restriction of the cotangent bundle to elliptic curves and Hilbert-Kunz fnctions
Holger Brenner, Georg Hein
We describe the possible restrictions of the cotangent bundle Ω_{\PP^N} to an elliptic curve C \subset \PP^N. We apply this in positive characteristic to the computation of the Hil…
A linear bound for Frobenius powers and an inclusion bound for tight closure
Holger Brenner
Let I denote an R_+ -primary homogeneous ideal in a normal standard-graded Cohen-Macaulay domain over a field of positive characteristic p. We give a linear degree bound for the Fr…
A Hilbert-Kunz criterion for solid closure in dimension two (characteristic zero)
Holger Brenner
Let I denote a homogeneous R_+-primary ideal in a two-dimensional normal standard-graded domain over an algebraically closed field of characteristic zero. We show that a homogeneou…
The rationality of the Hilbert-Kunz multiplicity in graded dimension two
Holger Brenner
We show that the Hilbert-Kunz multiplicity is a rational number for an R_+-primary homogeneous ideal I=(f_1, ..., f_n) in a two-dimensional graded domain R of finite type over an a…