Pullback Method with Applications to Severi--Brauer Fibrations
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911435785764864 |
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| author | Biswas, Mridul Ramachandran, Divyasree C Samanta, Biswanath |
| author_facet | Biswas, Mridul Ramachandran, Divyasree C Samanta, Biswanath |
| contents | Given a variety with a suitable Brauer class, we present a general pullback construction that produces varieties that has Brauer--Manin obstruction to the existence of rational points. We then study Severi--Brauer fibrations and their Brauer groups without relying on explicit defining equations. As a key application, we show that there exist Severi--Brauer fibrations with index one that fails Hasse principle. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_15125 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pullback Method with Applications to Severi--Brauer Fibrations Biswas, Mridul Ramachandran, Divyasree C Samanta, Biswanath Number Theory Algebraic Geometry Primary 14G05, Secondary 14G12, 11G35, 14J20, 11G25, 14F22 Given a variety with a suitable Brauer class, we present a general pullback construction that produces varieties that has Brauer--Manin obstruction to the existence of rational points. We then study Severi--Brauer fibrations and their Brauer groups without relying on explicit defining equations. As a key application, we show that there exist Severi--Brauer fibrations with index one that fails Hasse principle. |
| title | Pullback Method with Applications to Severi--Brauer Fibrations |
| topic | Number Theory Algebraic Geometry Primary 14G05, Secondary 14G12, 11G35, 14J20, 11G25, 14F22 |
| url | https://arxiv.org/abs/2410.15125 |