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Rationality Problem for Algebraic Tori

Rationality Problem for Algebraic Tori

          
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About the Book

The authors give the complete stably rational classification of algebraic tori of dimensions $4$ and $5$ over a field $k$. In particular, the stably rational classification of norm one tori whose Chevalley modules are of rank $4$ and $5$ is given.The authors show that there exist exactly $487$ (resp. $7$, resp. $216$) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension $4$, and there exist exactly $3051$ (resp. $25$, resp. $3003$) stably rational (resp. not stably but retract rational, resp. not retract rational) algebraic tori of dimension $5$.The authors make a procedure to compute a flabby resolution of a $G$-lattice effectively by using the computer algebra system GAP. Some algorithms may determine whether the flabby class of a $G$-lattice is invertible (resp. zero) or not. Using the algorithms, the suthors determine all the flabby and coflabby $G$-lattices of rank up to $6$ and verify that they are stably permutation. The authors also show that the Krull-Schmidt theorem for $G$-lattices holds when the rank $\leq 4$, and fails when the rank is $5$.

About the Author

Akinari Hoshi, Niigata University, Japan.Aiichi Yamasaki, Kyoto University, Japan.


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Product Details
  • ISBN-13: 9781470424091
  • Publisher: American Mathematical Society
  • Binding: Paperback
  • Language: English
  • Returnable: Y
  • Weight: 866 gr
  • ISBN-10: 1470424096
  • Publisher Date: 30 Jun 2017
  • Height: 254 mm
  • No of Pages: 215
  • Spine Width: mm
  • Width: 178 mm


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