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- W3011169905 abstract "Abstract Let $(K,mathcal {O},k)$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mo>(</mml:mo> <mml:mi>K</mml:mi> <mml:mo>,</mml:mo> <mml:mi>O</mml:mi> <mml:mo>,</mml:mo> <mml:mi>k</mml:mi> <mml:mo>)</mml:mo> </mml:math> be a p -modular system and assume k is algebraically closed. We show that if Λ is an $mathcal {O}$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>O</mml:mi> </mml:math> -order in a separable K -algebra, then $text {Pic}_{mathcal {O}}({Lambda })$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mrow> <mml:mtext>Pic</mml:mtext> </mml:mrow> <mml:mrow> <mml:mi>O</mml:mi> </mml:mrow> </mml:msub> <mml:mo>(</mml:mo> <mml:mi>Λ</mml:mi> <mml:mo>)</mml:mo> </mml:math> carries the structure of an algebraic group over k . As an application to the modular representation theory of finite groups, we show that a reduction theorem by Külshammer concerned with Donovan’s conjecture remains valid over $mathcal {O}$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>O</mml:mi> </mml:math> ." @default.
- W3011169905 created "2020-03-23" @default.
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- W3011169905 date "2020-03-16" @default.
- W3011169905 modified "2023-10-05" @default.
- W3011169905 title "The Picard Group of an Order and Külshammer Reduction" @default.
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- W3011169905 doi "https://doi.org/10.1007/s10468-020-09957-x" @default.
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