Relating test ideals and multiplier ideals
August 8 to August 12, 2011
American Institute of Mathematics,
San Jose, California
Karl Schwede and Kevin Tucker
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
Understanding F-jumping numbers of test ideals as the
characteristic p > 0 varies.
- Computing test ideals via finite extensions and regular
Test ideals and multiplier ideals in non-Q-Gorenstein rings.
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