A pathological case of the C1 conjecture in mixed characteristic
2018 ◽
Vol 167
(01)
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pp. 61-64
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AbstractLet 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.
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2012 ◽
Vol 23
(08)
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pp. 1250085
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2006 ◽
Vol 17
(01)
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pp. 45-63
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Keyword(s):
2001 ◽
Vol 63
(3)
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pp. 513-532
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2008 ◽
Vol 144
(3)
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pp. 721-733
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2018 ◽
Vol 2020
(15)
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pp. 4721-4775