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ETD

Digital archive of theses discussed at the University of Pisa

 

Thesis etd-05062024-113611


Thesis type
Tesi di dottorato di ricerca
Author
PIRANI, MATTIA
URN
etd-05062024-113611
Thesis title
Flasque quasi-resolutions and non-surjectivity of the evaluation map for homogeneous spaces
Academic discipline
MAT/03
Course of study
MATEMATICA
Supervisors
tutor Prof. Szamuely, Tamás
correlatore Prof. Gille, Philippe
Keywords
  • flasque quasi-resolutions
  • homogeneous spaces
  • R-equivalence
Graduation session start date
14/05/2024
Availability
Withheld
Release date
14/05/2027
Summary
The aim of this thesis is the study of R-equivalence classes of homogeneous spaces. For this purpose, the author introduces the concept of flasque quasi-resolution, which generalizes the better-known flasque resolutions introduced by Colliot-Thélène. The author employs them firstly to prove a stronger version of a theorem by Colliot-Thélène and Kunyavskii. Subsequently, the question arises whether the hypotheses of the proven theorem are necessary. Then, the author constructs two examples in which removing the hypotheses causes the claim to no longer hold, first on a field of cohomological dimension 2 and then on a 2-local field.
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