Relating test ideals and multiplier ideals

August 8 to August 12, 2011

at the

American Institute of Mathematics, San Jose, California

organized by

Karl Schwede and Kevin Tucker

Original Announcement

This workshop will be devoted to the the connection between two prominent and distinct means of measuring singularities: the multiplier ideal in complex algebraic geometry, and the test ideal in positive characteristic commutative algebra. These two concepts are related via "reduction to characteristic p" techniques. The subsequent interplay of geometric methods in characteristic zero and Frobenius techniques in positive characteristic continues to inspire new questions and results throughout numerous areas of mathematics, including algebraic geometry, commutative algebra, representation theory, and number theory.

Potential focus topics of this workshop include recent progress, new applications, and remaining open questions in the following areas:

These topics relate to several major open conjectures, namely weak verses strongly F-regularity, the direct summand conjecture and questions of ordinarity versus supersingularity for higher dimensional varieties.

Material from the workshop

A list of participants.

The workshop schedule.

A report on the workshop activities.

Papers arising from the workshop:

Depth of F-singularities and base change of relative canonical sheaves
by  Zsolt Patakfalvi and Karl Schwede,  J. Inst. Math. Jussieu 13 (2014), no. 1, 43-63  MR3134015
Semi-positivity in positive characteristics
by  Zsolt Patakfalvi,  Ann. Sci. Éc. Norm. Supér. (4) 47 (2014), no. 5, 991-1025  MR3294622
Hilbert-Kunz functions of 2 x 2 determinantal rings
by  Lance Edward Miller and Irena Swanson,  Illinois J. Math. 57 (2013), no. 1, 251-277  MR3224570
A Frobenius variant of Seshadri constants
by  Mircea Mustata and Karl Schwede,  Math. Ann. 358 (2014), no. 3-4, 861-878  MR3175143