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oai:repository.rice.edu:1911/1141912026-08-27T21:22:31Zcom_1911_8299col_1911_13110

Varilly-Alvarado, Anthony James, Austen A 2023-01-03T22:33:25Z 2023-01-03T22:33:25Z 2022-12 2022-12-02 December 2022 2023-01-03T22:33:25Z James, Austen A. "A Bayesian approach to computing Brauer groups of cubic surfaces." (2022) Diss., Rice University. https://hdl.handle.net/1911/114191 https://hdl.handle.net/1911/114191 We present an algorithm for computing the Brauer groups of cubic surfaces. The algorithm takes as input an equation for a cubic surface X and a confidence threshold 0.5 < r < 1 and outputs a candidate for the Brauer group of X and a confidence level > r for the result. The algorithm runs by sampling lifts of Frobenius at many primes of good reduction and relies on Chebotarev’s density theorem and Bayesian inference to produce, with confidence level > r, a subgroup of the Weyl group of E_6. This subgroup represents the action of Galois on the geometric Picard group of X, from which we compute the Brauer group of X. We give a description of this algorithm and a proof that it terminates, as well as an implementation in Magma. We also examine the speed of such an approach relative to existing methods and explore how the Bayesian technique of this algorithm can be applied to answer questions concerning the Galois and Brauer groups of other classes of surfaces. application/pdf eng Copyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder. arithmetic geometry brauer group cubic surfaces del pezzo surfaces algebraic geometry rational points A Bayesian approach to computing Brauer groups of cubic surfaces Thesis Text Mathematics Natural Sciences Rice University Doctoral Doctor of Philosophy open.access