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Search results for “positive characteristic”

67 results

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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A curiosity: “supersmooth” varieties

Theory

A rigidity condition on schemes, strictly stronger than smoothness, introduced with examples and a look at where it fails to be geometric — no known application, just a curiosity.
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IMO 1964

Problem sheet

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.
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IMO 1986

Problem sheet

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.
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IMO 1994

Problem sheet

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.
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IMO 1996

Problem sheet

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.
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IMO 2002

Problem sheet

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.
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IMO 1982

Problem sheet

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.
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IMO 1983

Problem sheet

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.
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IMO 1961

Problem sheet

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.
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IMO 1984

Problem sheet

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.
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IMO 1997

Problem sheet

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.
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IMO 2009

Problem sheet

50th International Mathematical Olympiad. Bremen, Germany, 2009.
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IMO 2013

Problem sheet

54th International Mathematical Olympiad. Colombia, 2013.
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IMO 2014

Problem sheet

55th International Mathematical Olympiad. Cape Town, South Africa, 2014.
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IMO 2024

Problem sheet

65th International Mathematical Olympiad, 2024.
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IMO 1965

Problem sheet

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.
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IMO 1975

Problem sheet

International mathematics competition for pre-university students, held annually since 1959. Six problems over two days.
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