Rationality Problem for Algebraic Tori

Released on by Akinari Hoshi
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  • Rationality Problem for Algebraic Tori Book Detail

  • Author : Akinari Hoshi
  • Release Date : 2017-07-13
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 228
  • ISBN 13 : 1470424096
  • File Size : 36,36 MB
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Rationality Problem for Algebraic Tori by Akinari Hoshi PDF Summary

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

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Rationality Problem for Algebraic Tori

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The authors give the complete stably rational classification of algebraic tori of dimensions and over a field . In particular, the stably rational classificatio

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Providing an overview of the state of the art on rationality questions in algebraic geometry, this volume gives an update on the most recent developments. It of