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37 results
The torsion component of the Picard scheme
2026OtherBogdan Zavyalov
Every finite flat commutative group scheme over a noetherian local ring is the torsion component of the Picard scheme of a smooth projective scheme with 3-dimensional fibers, built as a quotient of a complete intersection. An application: Hodge numbers that jump in a smooth projective family.
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500
Модели внимания и трансформеры
2026LectureКонстантин Вячеславович Воронцов
Модели внимания и трансформеры. Лекция курса «Машинное обучение» К. В. Воронцова. Задачи обработки и преобразования последовательностей (sequence to sequence).
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420
An example of a non-reduced Picard scheme
2026TheorySean Cotner
An example, due to Serre, of a smooth projective surface in positive characteristic whose Picard scheme fails to be reduced, worked out via the two governing dimension inequalities.
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170
Finite flat commutative group schemes embed locally into abelian schemes
2026TheorySean Cotner
A proof of Raynaud's theorem: every finite flat commutative group scheme over a locally noetherian base embeds, Zariski-locally, as a closed subgroup of an abelian scheme.
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150