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Reference for the algebro-geometric proof of Matsumoto theorem
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Matsumoto proved in his PhD thesis that if $F$ is a field than $K_2(F)=(F^*otimes F^*)/(xotimes (1-x))$. The original Matsumoto proof as it is written in Milnor's book on algebraic K-theory looks not really nice to me and one guy told me that there is another proof of this fact that uses "sheaves of groups on Severi-Brauer varieties" which seems nicer to me. This guy told me that it is due to Vaserstein (Ã’ðÑÂõрштõùý) but it seems that Vaserstein was interested in other questions and couldn't give this proof. Perhaps you know whom this proof belongs to and I'd be very grateful if you could give me the reference to the article.
ag.algebraic-geometry reference-request kt.k-theory-and-homology algebraic-k-theory
asked 2 hours ago
Anna Abasheva
639314
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up vote
7
down vote
favorite
Matsumoto proved in his PhD thesis that if $F$ is a field than $K_2(F)=(F^*otimes F^*)/(xotimes (1-x))$. The original Matsumoto proof as it is written in Milnor's book on algebraic K-theory looks not really nice to me and one guy told me that there is another proof of this fact that uses "sheaves of groups on Severi-Brauer varieties" which seems nicer to me. This guy told me that it is due to Vaserstein (Ã’ðÑÂõрштõùý) but it seems that Vaserstein was interested in other questions and couldn't give this proof. Perhaps you know whom this proof belongs to and I'd be very grateful if you could give me the reference to the article.
ag.algebraic-geometry reference-request kt.k-theory-and-homology algebraic-k-theory
asked 2 hours ago
Anna Abasheva
639314
add a comment |Â
up vote
7
down vote
favorite
up vote
7
down vote
favorite
Matsumoto proved in his PhD thesis that if $F$ is a field than $K_2(F)=(F^*otimes F^*)/(xotimes (1-x))$. The original Matsumoto proof as it is written in Milnor's book on algebraic K-theory looks not really nice to me and one guy told me that there is another proof of this fact that uses "sheaves of groups on Severi-Brauer varieties" which seems nicer to me. This guy told me that it is due to Vaserstein (Ã’ðÑÂõрштõùý) but it seems that Vaserstein was interested in other questions and couldn't give this proof. Perhaps you know whom this proof belongs to and I'd be very grateful if you could give me the reference to the article.
ag.algebraic-geometry reference-request kt.k-theory-and-homology algebraic-k-theory
asked 2 hours ago
Anna Abasheva
639314
Matsumoto proved in his PhD thesis that if $F$ is a field than $K_2(F)=(F^*otimes F^*)/(xotimes (1-x))$. The original Matsumoto proof as it is written in Milnor's book on algebraic K-theory looks not really nice to me and one guy told me that there is another proof of this fact that uses "sheaves of groups on Severi-Brauer varieties" which seems nicer to me. This guy told me that it is due to Vaserstein (Ã’ðÑÂõрштõùý) but it seems that Vaserstein was interested in other questions and couldn't give this proof. Perhaps you know whom this proof belongs to and I'd be very grateful if you could give me the reference to the article.
ag.algebraic-geometry reference-request kt.k-theory-and-homology algebraic-k-theory
ag.algebraic-geometry reference-request kt.k-theory-and-homology algebraic-k-theory
asked 2 hours ago
Anna Abasheva
639314
asked 2 hours ago
Anna Abasheva
639314
asked 2 hours ago
Anna Abasheva
639314
asked 2 hours ago
Anna Abasheva
639314
asked 2 hours ago
Anna Abasheva
639314
639314
add a comment |Â
add a comment |Â
1 Answer
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votes
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2
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Apparently, what this one guy meant is Merkurjev's proof of Merkurjev-Suslin theorem, which was writen down by A. R. Wadsworth and later by W. van der Kallen. The latter paper starts with the statement of Matsumoto theorem and the proof does indeed use cohomology of sheaves of K-groups on Severi-Brauer varieties.
As for the nicer proofs of Matsumoto theorem, one can take a look at A new approach to Matsumoto's theorem by K. Hutchinson or $(t^2−t)$-reciprocities on the affine line and Matsumoto's theorem by F. Keune.
answered 35 mins ago
Andrei Smolensky
1,0361022
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
2
down vote
Apparently, what this one guy meant is Merkurjev's proof of Merkurjev-Suslin theorem, which was writen down by A. R. Wadsworth and later by W. van der Kallen. The latter paper starts with the statement of Matsumoto theorem and the proof does indeed use cohomology of sheaves of K-groups on Severi-Brauer varieties.
As for the nicer proofs of Matsumoto theorem, one can take a look at A new approach to Matsumoto's theorem by K. Hutchinson or $(t^2−t)$-reciprocities on the affine line and Matsumoto's theorem by F. Keune.
answered 35 mins ago
Andrei Smolensky
1,0361022
add a comment |Â
up vote
2
down vote
Apparently, what this one guy meant is Merkurjev's proof of Merkurjev-Suslin theorem, which was writen down by A. R. Wadsworth and later by W. van der Kallen. The latter paper starts with the statement of Matsumoto theorem and the proof does indeed use cohomology of sheaves of K-groups on Severi-Brauer varieties.
As for the nicer proofs of Matsumoto theorem, one can take a look at A new approach to Matsumoto's theorem by K. Hutchinson or $(t^2−t)$-reciprocities on the affine line and Matsumoto's theorem by F. Keune.
answered 35 mins ago
Andrei Smolensky
1,0361022
add a comment |Â
up vote
2
down vote
up vote
2
down vote
Apparently, what this one guy meant is Merkurjev's proof of Merkurjev-Suslin theorem, which was writen down by A. R. Wadsworth and later by W. van der Kallen. The latter paper starts with the statement of Matsumoto theorem and the proof does indeed use cohomology of sheaves of K-groups on Severi-Brauer varieties.
As for the nicer proofs of Matsumoto theorem, one can take a look at A new approach to Matsumoto's theorem by K. Hutchinson or $(t^2−t)$-reciprocities on the affine line and Matsumoto's theorem by F. Keune.
answered 35 mins ago
Andrei Smolensky
1,0361022
Apparently, what this one guy meant is Merkurjev's proof of Merkurjev-Suslin theorem, which was writen down by A. R. Wadsworth and later by W. van der Kallen. The latter paper starts with the statement of Matsumoto theorem and the proof does indeed use cohomology of sheaves of K-groups on Severi-Brauer varieties.
As for the nicer proofs of Matsumoto theorem, one can take a look at A new approach to Matsumoto's theorem by K. Hutchinson or $(t^2−t)$-reciprocities on the affine line and Matsumoto's theorem by F. Keune.
answered 35 mins ago
Andrei Smolensky
1,0361022
answered 35 mins ago
Andrei Smolensky
1,0361022
answered 35 mins ago
Andrei Smolensky
1,0361022
answered 35 mins ago
Andrei Smolensky
1,0361022
1,0361022
add a comment |Â
add a comment |Â
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