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- W2892778690 abstract "Abstract Let k be an algebraically closed field, $$lne {{,textrm{char},}}k$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>l</mml:mi> <mml:mo>≠</mml:mo> <mml:mrow> <mml:mspace /> <mml:mtext>char</mml:mtext> <mml:mspace /> </mml:mrow> <mml:mi>k</mml:mi> </mml:mrow> </mml:math> a prime number, and X a quasi-projective scheme over k . We show that the étale homotopy type of the d th symmetric power of X is $$textbf{Z}/l$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>Z</mml:mi> <mml:mo>/</mml:mo> <mml:mi>l</mml:mi> </mml:mrow> </mml:math> -homologically equivalent to the d th strict symmetric power of the étale homotopy type of X . We deduce that the $$textbf{Z}/l$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>Z</mml:mi> <mml:mo>/</mml:mo> <mml:mi>l</mml:mi> </mml:mrow> </mml:math> -local étale homotopy type of a motivic Eilenberg–Mac Lane space is an ordinary Eilenberg–Mac Lane space." @default.
- W2892778690 created "2018-10-05" @default.
- W2892778690 creator A5068014837 @default.
- W2892778690 date "2023-03-28" @default.
- W2892778690 modified "2023-09-26" @default.
- W2892778690 title "The étale symmetric Künneth theorem" @default.
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- W2892778690 doi "https://doi.org/10.1007/s00209-023-03246-1" @default.
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