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DTSTAMP:20250310T124529Z
CREATED:20241126T092815Z
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UID:48140-1743170400-1743174000@lmno.unicaen.fr
SUMMARY:Séminaire TNGA : Vaidehee Thatte
DESCRIPTION:Oratrice : Vaidehee Thatte (King’s College London) \n\n\n\nTitre : Ramification Theory for Henselian Valued Fields \n\n\n\nRésumé : Ramification theory serves the dual purpose of a diagnostic tool and treatment by helping us locate\, measure\, and treat the anomalous behaviour of mathematical objects. In the classical setup\, the degree of a finite Galois extension of « nice » fields splits up neatly into the product of two well-understood numbers (ramification index and inertia degree) that encode how the base field changes. \n\n\n\nIn the general case\, however\, a third factor called the defect (or ramification deficiency) can pop up. The defect is a mysterious phenomenon and the main obstruction to several long-standing open problems\, such as obtaining resolution of singularities. The primary reason is\, roughly speaking\, that the classical strategy of « objects become nicer after finitely many adjustments » fails when the defect is non-trivial. I will discuss my previous and ongoing work in ramification theory in this setting; in particular\, it allows us to understand and treat the defect. Background in ramification theory or valuation theory is not assumed.
URL:https://lmno.unicaen.fr/evenement/seminaire-tnga-vaidehee-thatte/
CATEGORIES:Séminaire,Théorie des nombres
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