A pathological case of the $C_1$ conjecture in mixed characteristic
| Autor: | Kaur, Inder |
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| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1017/S0305004118000178 |
| Popis: | Let $K$ be a field of characteristic 0. Fix integers $r,d$ coprime with $r \geq 2$. Let $X_K$ be a smooth, projective, geometrically connected curve of genus $g \geq 2$ defined over K. Assume there exists a line bundle $L_K$ on $X_K$ of degree $d$. In this article we prove the existence of a stable locally free sheaf on $X_K$ with rank $r$ and determinant $L_K$. This trivially proves the $C_1$ conjecture in mixed characteristic for the moduli space of stable locally free sheaves of fixed rank and determinant over a smooth, projective curve. Comment: Published in Mathematical Proceedings of the Cambridge Philosophical Society |
| Databáze: | arXiv |
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