Интегралы, содержащие логарифм
2026СправочникSergey
Справочная таблица неопределённых интегралов от выражений с натуральным логарифмом.
0
230
Результаты поиска по запросу «natural logarithm»
22 результата
A non-Noetherian local ring with finitely generated maximal ideal
2026ЗаметкиBogdan Zavyalov
A complete local ring with a finitely generated maximal ideal is Noetherian. Drop completeness and it fails: an ultraproduct construction gives a non-Noetherian local ring whose maximal ideal is principal.
0
340
Fun example: empty colimit does not commute with empty limit
2026ЗаметкиBogdan Zavyalov
Why the definition of a filtered category insists on non-emptiness: the empty colimit fails to commute with the empty limit, and that is the only failure.
0
310
Определитель через перестановки
2026ТеорияSergey
Прямое определение определителя через перестановки: инверсии, чётность и сумма из n! слагаемых.
0
170
An example of a non-reduced Picard scheme
2026ТеорияSean 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.
1
170
Finite flat commutative group schemes embed locally into abelian schemes
2026ТеорияSean 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.
1
150
The torsion component of the Picard scheme
2026ДругоеBogdan 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.
1
500