The Chern class map on abelian surfaces

We examine the Chern class map ${c}_{1}: {\rm NS}(S)/p{\rm NS}(S) \rightarrow {\rm H}^{1}(S, Ω^{1}_{S})$ for an abelian surface $S$ in characteristic $p \geq 3$, and give a basis of the kernel $c_{1}$ for the superspecial abelian surface.

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