Search results for “algebraic geometry”

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@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.

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.

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.

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.

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.

CMI 2000, The Millennium Prize Problems

2026Problem sheet

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

The Steinberg Representation

Theory

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.