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3 results

  • Lefschetz theorems in flat cohomology and applications

  • Part of
  • Sean Cotner, Bogdan Zavyalov
  • Journal:
    Compositio Mathematica / Volume 160 / Issue 8 / August 2024
    Published online by Cambridge University Press:
    11 September 2024, pp. 1850-1870
    Print publication:
    August 2024
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  • We prove a version of the Lefschetz hyperplane theorem for fppf cohomology with coefficients in any finite commutative group scheme over the ground field. As consequences, we establish new Lefschetz results for the Picard scheme.

  • Corrigendum: The affine part of the Picard scheme

  • Part of
  • Thomas Geisser
  • Journal:
    Compositio Mathematica / Volume 157 / Issue 10 / October 2021
    Published online by Cambridge University Press:
    06 October 2021, pp. 2338-2340
    Print publication:
    October 2021
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  • We give a corrected version of Theorem 3, Lemma 4, and Proposition 9 in the above-mentioned paper, which are incorrect as stated (as was pointed out by O. Gabber).

  • The affine part of the Picard scheme

  • Part of
  • Thomas Geisser
  • Journal:
    Compositio Mathematica / Volume 145 / Issue 2 / March 2009
    Published online by Cambridge University Press:
    01 March 2009, pp. 415-422
    Print publication:
    March 2009
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  • We describe the maximal torus and maximal unipotent subgroup of the Picard variety of a proper scheme over a perfect field.