2021/05/14 by Hara Charalambous, Charalambous, Hara, Kostas Karagiannis +5
Mathematics · #11G99 #11L40 #13D40 #13N05 #14F10 #14H37 #20C15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Group Theory (math.GR) #Number Theory (math.NT) #math.AC #math.AG #math.GR #math.NT #msc:11G99 #msc:11L40 #msc:13D40 #msc:13N05 #msc:14F10 #msc:14H37 #msc:20C15
paper · pdf · doi:10.48550/arxiv.2105.06945
openalex publication_date 2021/05/14 · arxiv created 2021/09/01 · arxiv updated 2021/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider a Fermat curve Fn:xn+yn+zn=1 over an algebraically closed field k of characteristic p≥0 and study the action of the automorphism group G=(ℤ/nℤ×ℤ/nℤ)\rtimes S3 on the canonical ring R=\bigoplus H0(Fn,ΩFn⊗ m) when p>3, p\nmid n and n-1 is not a power of p. In particular, we explicitly determine the classes [H0(Fn,ΩFn⊗ m)] in the Grothendieck group K0(G,k) of finitely generated k[G]-modules, describe the respective equivariant Hilbert series HR,G(t) as a rational function, and use our results to write a program in Sage that computes HR,G(t) for an arbitrary Fermat curve.