10:00 AM - 11:00 AM
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Remarks on big Cohen-Macaulay algebras and on ramification over log-regular rings
Ofer Gabber (Institut des Hautes Études Scientifiques (IHES))
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
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- Supplements
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Gabber
73 KB application/pdf
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Notes
906 KB application/pdf
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11:00 AM - 11:30 AM
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Break
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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11:30 AM - 12:30 PM
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Big Cohen-Macaulay modules, morphisms of perfect complexes, and intersection theorems
Luchezar Avramov (University of Nebraska)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
The talk concerns morphisms between perfect complexes over commutative noetherian rings. The central result is a criterion for the tensor-nilpotence of such morphisms, in terms of numerical invariants of complexes known as levels. The proof uses the existence of big Cohen-Macaulay modules. Applications to local rings include a strengthening of the Improved New Intersection Theorem, and short direct proofs of several results equivalent to it. The results come from recent joint work with Iyengar and Neeman; see https://arxiv.org/abs/1711.04052
- Supplements
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12:30 PM - 02:30 PM
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Lunch
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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--
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02:30 PM - 03:30 PM
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Perfectoid multiplier/test ideals and symbolic powers
Linquan Ma (Purdue University)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
Inspired by the solution of the direct summand conjecture, we introduce perfectoid multiplier/test ideals in mixed characteristic. As an application, we prove the uniform bound on the growth of symbolic powers in regular local rings of mixed characteristic analogous to results of Ein--Lazarsfeld--Smith and Hochster--Huneke in equal characteristic. This is joint work with Karl Schwede
- Supplements
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Ma
397 KB application/pdf
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03:30 PM - 04:00 PM
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Tea
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- Location
- SLMath: Atrium
- Video
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- Abstract
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- Supplements
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04:00 PM - 05:00 PM
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Singularities mod p, and singularities in mixed characteristic
Karl Schwede (University of Utah)
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- Location
- SLMath: Eisenbud Auditorium
- Video
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- Abstract
Suppose that R is a local ring of mixed characteristic. Using recent breakthrough results of André on the existence of big Cohen-Macaulay algebras, we defined a mixed characteristic analog of the multiplier ideal / test ideal and show it satisfies many of the same formal properties as its equal characteristic brethren. Using the same ideas, we show that if R is mixed characteristic and local and R/pR has F-rational or F-regular singularities, then R itself has analgous singularities in mixed characteristic. This is joint work with Linquan Ma
- Supplements
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