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Search results for “algebraic-geometry”

49 results

@sean_cotner

NSF Research Fellow and postdoc at the University of Bonn. Previously an NSF Research Fellow and Postdoctoral Assistant Professor at the University of Michigan, and before that a graduate student at Stanford, advised by Brian Conrad. Interested in arithmetic geometry, algebraic groups (broadly construed), and integral questions connected to the local Langlands program.

Some examples of algebraic groups

2026TheorySean Cotner

Two pathological phenomena for algebraic groups over general bases — a group degenerating between the multiplicative and additive group across a DVR, and a non-affine identity component — built as centralizers in SL_n.

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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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A curiosity: “supersmooth” varieties

2026TheorySean Cotner

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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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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IMO 2008

2026Problem sheet

49th International Mathematical Olympiad. Madrid, Spain, 10-22 July 2008.
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IMO 2009

2026Problem sheet

50th International Mathematical Olympiad. Bremen, Germany, 2009.
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IMO 2012

2026Problem sheet

53rd International Mathematical Olympiad. Mar del Plata, Argentina, 2012.
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IMO 2023

2026Problem sheet

64th International Mathematical Olympiad. Chiba, Japan, 2023.
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IMO 2007

2026Problem sheet

48th International Mathematical Olympiad, 2007.
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IMO 2013

2026Problem sheet

54th International Mathematical Olympiad. Colombia, 2013.
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IMO 2015

2026Problem sheet

56th International Mathematical Olympiad. Thailand, 2015.
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IMO 2016

2026Problem sheet

57th International Mathematical Olympiad. Hong Kong, 2016.
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IMO 2018

2026Problem sheet

59th International Mathematical Olympiad. Cluj-Napoca, Romania, 2018.
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IMO 2019

2026Problem sheet

60th International Mathematical Olympiad, 2019.
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IMO 2010

2026Problem sheet

51st International Mathematical Olympiad, 2010.
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IMO 2014

2026Problem sheet

55th International Mathematical Olympiad. Cape Town, South Africa, 2014.
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IMO 2020

2026Problem sheet

61st International Mathematical Olympiad, 2020.
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