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On Noether's Degree Bound for Finite Group Schemes

Published 30 May 2025 in math.AC | (2505.24752v1)

Abstract: This paper establishes Noether's classical degree bound $\beta(G) \le |G|$ for finite and linearly reductive group schemes. On the other hand, we provide examples of infinitesimal group schemes where $\beta(G)$ is unbounded. We also generalize Molien's formula to finite and linearly reductive group schemes.

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