The modified explicit Brumer–Stark unit conjecture

Let FpF_p^* be the relevant local multiplicative group and let F^p=Fp^Zp\widehat{F}_p^*=F_p^*\widehat\otimes\mathbf{Z}_p. Define vp(b)anF^pv_p(\mathfrak b)^{\mathrm{an}}\in\widehat{F}_p^* from the explicitly constructed quantities up(b)anu_p(\mathfrak b)^{\mathrm{an}}, and let upu_{\mathfrak p} be the Brumer–Stark unit. Modified explicit Brumer–Stark conjecture. One should have

σb(up)=vp(b)anin F^p.\sigma_{\mathfrak b}(u_{\mathfrak p})=v_p(\mathfrak b)^{\mathrm{an}}\quad\text{in }\widehat{F}_p^*.

This is presented as a slightly easier form of the preceding explicit formula conjecture; the source notes that the corresponding inversion property for vpv_p holds unconditionally. The source gives no resolution status.

Sources & referencesView supporting material

Primary source

Samit Dasgupta and Mahesh Kakde, “On the Brumer-Stark Conjecture and Refinements”, arXiv:2204.09037 (2022).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.