Αποθηκεύτηκε σε:
| Κύριος συγγραφέας: | |
|---|---|
| Μορφή: | Preprint |
| Έκδοση: |
2022
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| Θέματα: | |
| Διαθέσιμο Online: | https://arxiv.org/abs/2212.03213 |
| Ετικέτες: |
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Πίνακας περιεχομένων:
- In this article, we extend an argument of Vogtmann in order to show homology stability of the Euclidean orthogonal group $O_n(A)$ when $A$ is a valuation ring subject to arithmetic conditions on either its residue or its quotient field. In particular, it is shown that if $A$ is a henselian valuation ring, then the groups $O_n(A)$ exhibit homology stability if the residue field of $A$ has finite Pythagoras number. Our results include those of Vogtmann, and hold with various twisted coefficients. Using these results, we give analogues for fields $F\neq\mathbb R$ of some computations that appear in the study of scissor congruences.