Sean Cotner

@sean_cotner

NSF Research Fellow and Postdoc at the University of Bonn

1 follower15 works

The Steinberg Representation

Aug 24, 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.

390

Some examples of algebraic groups

Aug 24, 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.

320

Finite flat commutative group schemes embed locally into abelian schemes

Aug 24, 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.

270

An example of a non-reduced Picard scheme

Aug 24, 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.

280

A curiosity: “supersmooth” varieties

Aug 24, 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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A corrigendum to this paper is published on the author's homepage.

Sean Cotner

The Steinberg Representation

Some examples of algebraic groups

Finite flat commutative group schemes embed locally into abelian schemes

An example of a non-reduced Picard scheme

A curiosity: “supersmooth” varieties

Central isogenies and conjugacy classes in reductive groups

Connected components of the moduli space of L-parameters

Lifting G-Valued Galois Representations when ℓ ≠ p

Morphisms of Character Varieties

Lefschetz theorems in flat cohomology and applications

Hom schemes for algebraic groups

Centralizers of sections of a reductive group scheme

The Steinberg Representation

Some examples of algebraic groups

Finite flat commutative group schemes embed locally into abelian schemes

An example of a non-reduced Picard scheme

A curiosity: “supersmooth” varieties

Central isogenies and conjugacy classes in reductive groups

Connected components of the moduli space of L-parameters

Lifting G-Valued Galois Representations when ℓ ≠ p

Morphisms of Character Varieties

Lefschetz theorems in flat cohomology and applications

Hom schemes for algebraic groups

Centralizers of sections of a reductive group scheme