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A pathological case of the C1 conjecture in mixed characteristic

Published online by Cambridge University Press:  05 April 2018

INDER KAUR
INDER KAUR*
Affiliation:
Instituto Nacional de Matemática Pura e Aplicada, Estr. Dona Castorina, 110 - Jardim Botânico, Rio de Janeiro - RJ, 22460-320, Brazil. e-mail: [email protected]
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Abstract

Let K be a field of characteristic 0. Fix integers r, d coprime with r ⩾ 2. Let XK be a smooth, projective, geometrically connected curve of genus g ⩾ 2 defined over K. Assume there exists a line bundle ${\cal L}_K$ on XK of degree d. In this paper we prove the existence of a stable locally free sheaf on XK with rank r and determinant ${\cal L}_K$. This trivially proves the C1 conjecture in mixed characteristic for the moduli space of stable locally free sheaves of fixed rank and determinant over a smooth, projective curve.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 167 , Issue 1 , July 2019 , pp. 61 - 64
Copyright
Copyright © Cambridge Philosophical Society 2018 

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References

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