Existence of birational small Cohen-Macaulay modules over biquadratic extensions in mixed characteristic
| Autor: | Prashanth Sridhar |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Algebra and Number Theory Mathematics::Commutative Algebra Image (category theory) 010102 general mathematics Closure (topology) Field (mathematics) Square-free integer Regular local ring Extension (predicate logic) Mathematics - Commutative Algebra Commutative Algebra (math.AC) Subring 01 natural sciences Mathematics - Algebraic Geometry 0103 physical sciences FOS: Mathematics 010307 mathematical physics 13C14 (Primary) 13B22 13C10 13C15 13D22 13H05 0101 mathematics Algebraic Geometry (math.AG) Quotient Mathematics |
| Zdroj: | Journal of Algebra. 582:100-116 |
| ISSN: | 0021-8693 |
| Popis: | Let $S$ be an unramified regular local ring of mixed characteristic two and $R$ the integral closure of $S$ in a biquadratic extension of its quotient field obtained by adjoining roots of sufficiently general square free elements $f,g\in S$. Let $S^2$ denote the subring of $S$ obtained by lifting to $S$ the image of the Frobenius map on $S/2S$. When at least one of $f,g\in S^2$, we characterize the Cohen-Macaulayness of $R$ and show that $R$ admits a birational small Cohen-Macaulay module. It is noted that $R$ is not automatically Cohen-Macaulay in case $f,g\in S^2$ or if $f,g\notin S^2$. Comment: Final version, to appear in Journal of Algebra; minor changes, unabbreviated title, updated references |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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