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Picard group of connected affine algebraic group

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arxiv 2302.13374 v2 pith:I6YTVL6H submitted 2023-02-26 math.AG

Vladimir L. Popov This is my paper · ORCID
classification math.AG
keywords groupalgebraicaffineconnectedmathscrpicardderivedfundamental
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abstract

We prove that the Picard group of a connected affine algebraic group $G$ is isomorphic to the fundamental group of the derived subgroup of the reductive algebraic group $G/{\mathscr R}_u(G)$, where ${\mathscr R}_u(G)$ is the unipotent radical of $G$.

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  1. A refinement of the coherence conjecture of Pappas and Rapoport

    math.AG 2024-12 conditional novelty 7.0 of 10

    The paper refines Zhu's proof of the Pappas-Rapoport coherence conjecture from an equality of dimensions to isomorphisms of representations, with applications to affine Demazure modules.

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