Hartl's arcwise connectedness conjecture for the intrinsic period domain

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Let F˘b0\breve{\cal{F}}^0_b be the intrinsic open E˘\breve E-analytic subspace of the weakly admissible period space F˘bwa\breve{\cal{F}}^{wa}_b constructed in the paper.

Hartl's connectedness conjecture. The space F˘b0\breve{\cal{F}}^0_b is arcwise connected.

The paper proves that F˘b0\breve{\cal{F}}^0_b contains the relevant finite-extension-valued points and explains that the finitely generated value-group conjecture would imply arcwise connectedness. The assertion itself remains unproved there.

References

Primary source

Urs Hartl, “On a Conjecture of Rapoport and Zink”, arXiv:math/0605254 (2013).

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