Seminar
| Parent Program: | -- |
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| Location: | SLMath: Online/Virtual |
To attend this seminar, you must register in advance, by clicking HERE.
Title: The quest for F-rational signature
Abstract: Strongly F-regular singularities are one of the fundamental classes of singularities defined by the properties of Frobenius endomorphism. This class of mild singularities can be detected using F-signature, an invariant of a local ring with many good properties. Through this connection we obtain a powerful tool for studying strongly F-regular singularities, for example, several results on "mildness" of F-regular can be quantified using F-signature.
Another fundamental class of singularities in positive characteristic are F-rational singularities. While generally more severe, this class of singularities is in many aspects analogous to strongly F-regular singularities and can be even understood by "moving" the definition of F-regularity to take place in the dualizing module. Naturally, there has been interest in adapting the definition of F-signature to work with F-rational singularities.
While there is no complete solution yet, I am convinced that such a theory should exist. As my evidence, I will present results of a joint work with Kevin Tucker, and prior works of Hochster and Yao, and Sannai.
My talk will be self-contained. I will discuss all necessary background, such as definitions, properties, and relations between these notions, in the first half and then proceed to more technical results in the second half.
Speaker: Ilya Smirnov, Stockholm University
The Quest For F-Rational Signature
To attend this seminar, you must register in advance, by clicking HERE.
Abstract: Strongly F-regular singularities are one of the fundamental classes of singularities defined by the properties of Frobenius endomorphism. This class of mild singularities can be detected using F-signature, an invariant of a local ring with many good properties. Through this connection we obtain a powerful tool for studying strongly F-regular singularities, for example, several results on "mildness" of F-regular can be quantified using F-signature.
Another fundamental class of singularities in positive characteristic are F-rational singularities. While generally more severe, this class of singularities is in many aspects analogous to strongly F-regular singularities and can be even understood by "moving" the definition of F-regularity to take place in the dualizing module. Naturally, there has been interest in adapting the definition of F-signature to work with F-rational singularities.
While there is no complete solution yet, I am convinced that such a theory should exist. As my evidence, I will present results of a joint work with Kevin Tucker, and prior works of Hochster and Yao, and Sannai.
My talk will be self-contained. I will discuss all necessary background, such as definitions, properties, and relations between these notions, in the first half and then proceed to more technical results in the second half.
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Notes
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