Timeline for Reference request: Given a non-degenerate integral quadratic lattice $L,q$ over a PID, the quotient $L^*/L$ is given by SNF of $q$
Current License: CC BY-SA 4.0
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| Sep 25, 2021 at 12:02 | comment | added | Will Sawin | @user148575 In the degenerate case, $L_1^*$ looks like $a_1^{-1} e_1 R + \dots + a_r^{-1} R + K E_{r+1} + \dots + K e_n$ and the quotient contains copies of $K/R$. Other than that, the argument works. | |
| Sep 25, 2021 at 4:16 | comment | added | user148575 | After getting back to this question, I'm thinkind: Where do you actually use non-degeneration? I think if $a_r$ is your last non-zero diagonal entry in the SNF, then $a_1^{-1}e_1,…,a_r^{-1}e_r,e_{r+1},\dots,e_n$ is still a base for $L_1^*$, no? | |
| Jul 28, 2021 at 14:08 | history | edited | Will Sawin | CC BY-SA 4.0 |
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| Jul 28, 2021 at 14:07 | comment | added | user148575 | Thanks for the great answer! (typo: "Smith normal form of $q$" -> "Smith normal form of $b$"). | |
| Jul 28, 2021 at 14:00 | vote | accept | user148575 | ||
| Jul 28, 2021 at 13:58 | history | answered | Will Sawin | CC BY-SA 4.0 |