Timeline for Lattices as invertible modules.
Current License: CC BY-SA 3.0
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| May 17, 2013 at 18:07 | history | edited | user9072 |
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| May 17, 2013 at 15:33 | comment | added | Jiangwei Xue | @nosr, do you mean Shimura's book "Introduction to the arithmetic theory of automorphic functions"? | |
| May 17, 2013 at 13:30 | comment | added | user28172 | No. The case of quadratic fields is misleading, or rather has a special property that fails in higher degree: the ring of integers is monogenic over $\mathbf{Z}$. Once you drop that property, the invertibility can fail (and all orders in rings of integers of number fields are Cohen-Macaulay). I think there are counterexamples given in Shimura's introductory book on modular forms, around where he discusses the invertibility in the quadratic case. | |
| May 17, 2013 at 8:10 | history | asked | Jiangwei Xue | CC BY-SA 3.0 |