Search results for “algebraic geometry”

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55 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.

180

Arithmetic Properties Of l-adic Etale Cohomology and Nearby Cycles of Rigid-Analytic Spaces

2023PreprintDavid Hansen, Bogdan Zavyalov

Recommended for publication at the Journal of Algebraic Geometry; under review.

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.

500

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.

120

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.

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.

150

CMI 2000, The Millennium Prize Problems

2026Problem sheet

The Millennium Meeting, Paris, 24 May 2000, at which the seven problems were announced.

360

The Steinberg Representation

2026TheorySean Cotner

An introduction to the Steinberg representation of a finite group of Lie type — its alternating-sum construction from parabolic inductions, worked out explicitly for SL_2.

270

Determinant

2026TheorySergey

The determinant of a square matrix — its meaning, minors and cofactors, Laplace expansion, and computation methods.

190

Linear algebra and analytic geometry. Vector algebra

2026Problem sheetSergey

Vectors in coordinates: dividing a segment, midpoints of sides, the angle between vectors, the cross product and the scalar triple product.

180

IMO 2008

2026Problem sheet

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

230

IMO 2009

2026Problem sheet

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

340

IMO 2012

2026Problem sheet

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

290

IMO 2023

2026Problem sheet

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

430

IMO 2007

2026Problem sheet

48th International Mathematical Olympiad, 2007.

280

IMO 2013

2026Problem sheet

54th International Mathematical Olympiad. Colombia, 2013.

350

IMO 2015

2026Problem sheet

56th International Mathematical Olympiad. Thailand, 2015.

320

IMO 2016

2026Problem sheet

57th International Mathematical Olympiad. Hong Kong, 2016.

440

IMO 2018

2026Problem sheet

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

410