Geodesic
Reduced Whitehead groups of prime exponent algebras over $p$-adic curves
Documenta mathematica, Tome 26 (2021), pp. 337-413.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Let $F$ be the function field of a curve over a $p$-adic field. Let $D/F$ be a central division algebra of prime exponent $\ell$ which is different from $p$. Assume that $F$ contains a primitive $\ell^{2th}$ root of unity. Then the abstract group $\mathrm{SK}_1(D):=\frac{\mathrm{SL}_1(D)}{\left[D^{\ast}, D^{\ast}\right]}$ is trivial.
Classification : 16K20, 16K50, 11R58, 14H25, 14H05
Keywords: reduced Whitehead groups, Tannaka-Artin problem, patching, \(\mathrm{SK}_1\), function fields of \(p\)-adic curves 
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     author = {Bhaskhar, Nivedita},
     title = {Reduced {Whitehead} groups of prime exponent algebras over \(p\)-adic curves},
     journal = {Documenta mathematica},
     pages = {337--413},
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     volume = {26},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a48/}
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Bhaskhar, Nivedita. Reduced Whitehead groups of prime exponent algebras over \(p\)-adic curves. Documenta mathematica, Tome 26 (2021), pp. 337-413. http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a48/