The Cohen-Macaulay property of invariant rings over ring of integers of a global field
Autor: | Puthenpurakal, Tony J. |
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Rok vydání: | 2024 |
Předmět: | |
Druh dokumentu: | Working Paper |
Popis: | Let $A$ be the ring of integers of global field $K$. Let $G \subseteq GL_2(A)$ be a finite group. Let $G$ act linearly on $R = A[X,Y]$ (fixing $A$). Let $R^G$ be the ring of invariants. In the equi-characteristic case we prove $R^G$ is Cohen-Macaulay. In mixed characteristic case we prove that if for all primes $p$ dividing $|G|$ the Sylow $p$-subgroup of $G$ has exponent $p$ then $R^G$ is Cohen-Macaulay. We prove a similar case if for all primes $p$ dividing $|G|$ the prime $p$ is un-ramified in $K$. |
Databáze: | arXiv |
Externí odkaz: |
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