曲线 cohomology 的不可分解直和项
Indecomposable direct summands of cohomologies of curves
AI总结：
本文研究带群作用的光滑射影曲线 cohomology 的不可分解直和项，通过分析 Z/p × Z/p-覆盖族并完全描述其 cohomology，证明通常存在无穷多个这样的直和项。
摘要：
具有非循环 Sylow p-子群的群在特征 p 的域上有太多表示，难以完全描述。一个自然的问题是：来自带群作用的代数簇的表示世界是否与所有模表示的世界一样广阔。本文探讨了带群作用的光滑射影曲线的 cohomology 的可能“构建块”（不可分解直和项）。我们证明通常存在无穷多个这样的可能直和项。为证明这一点，我们研究了一族 Z/p × Z/p-覆盖，并完全描述了该族成员的 cohomology。
英文摘要：
Groups with a non-cyclic Sylow $p$-subgroup have too many representations over a field of characteristic~$p$ to describe them fully. A~natural question arises, whether the world of representations coming from algebraic varieties with a group action is as vast as the realm of all modular representations. In this article, we explore the possible ``building blocks'' (the indecomposable direct summands) of cohomologies of smooth projective curves with a group action. We show that usually there are infinitely many such possible summands. To prove this, we study a family of $\mathbb Z/p \times \mathbb Z/p$-covers and describe the cohomologies of the members of this family completely.
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