A cohomological obstruction to the Hasse principle for homogeneous spaces | Zendy

Mikhail Borovoi | Zendy

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A cohomological obstruction to the Hasse principle for homogeneous spaces

Author(s) -

Mikhail Borovoi

Publication year - 1999

Publication title -

mathematische annalen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.235

H-Index - 75

eISSN - 1432-1807

pISSN - 0025-5831

DOI - 10.1007/s002080050304

Subject(s) - mathematics , hasse principle , abelian group , pure mathematics , brauer group , algebraic number , abelian variety , homogeneous , algebraic number field , mathematical analysis , combinatorics

For a homogeneous space with connected or abelian stabilizer of a connected linear algebraic group defined over a num- ber field, a cohomological obstruction to the Hasse principle is defined in terms of Galois hypercohomology with coecients in a complex of two abelian algebraic groups. This obstruction is proved to be the only obstruction to the Hasse principle. It is proved that up to sign this cohomological obstruction coincides with the Brauer-Manin obstruction.

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