Strongly F-regular rings, maximal Cohen-Macaulay modules, and the F-signature
Thomas Polstra (University of Virgina)
Abstract: The singularities of a local prime characteristic ring are best understood through the behavior of the Frobenius endomorphism. A singularity class of central focus is the class of strongly $F$-regular rings. Examples of strongly $F$-regular rings include normal affine toric rings, direct summands of regular rings, and determinantal rings. Every strongly $F$-regular ring enjoys the property of being a normal Cohen-Macaulay domain. In particular, the study of finitely generated maximal Cohen-Macaulay modules over such rings is a warranted venture. We will demonstrate a surprising uniform behavior enjoyed by the category of maximal Cohen-Macaulay modules over a strongly $F$-regular local ring. Consequently, we can redrive Aberbach and Leuschke's theorem that the $F$-signature of a strongly $F$-regular ring is positive in a novel and elementary manner. Time permitting, we will present applications on the structure of the divisor class group of a local strongly $F$-regular ring.
Mathematics
Audience: advanced learners
IIT Bombay Virtual Commutative Algebra Seminar
Series comments: Note: To get meeting ID,fill the Google form on the web-site of the series sites.google.com/view/virtual-comm-algebra-seminar/home
Organizers: | Jugal Kishore Verma*, Kriti Goel*, Parangama Sarkar, Shreedevi Masuti |
Curator: | Saipriya Dubey* |
*contact for this listing |