Tohoku Mathematical Journal
2020
December
SECOND SERIES VOL. 72, NO. 4

Tohoku Math. J.
72 (2020), 537-550

Title GENERALIZED CARTAN-BEHNKE-STEIN'S THEOREM AND $Q$-PSEUDOCONVEXITY IN A STEIN MANIFOLD

Author Yuichiro Hoshi

(Received January 10, 2019, revised September 9, 2019)
Abstract. Schmidt and Stix proved that every smooth variety over a field finitely generated over the field of rational numbers has an open basis for the Zariski topology consisting of ``anabelian'' varieties. This was predicted by Grothendieck in his letter to Faltings. In the present paper, we generalize this result to smooth varieties over generalized sub-$p$-adic fields. Moreover, we also discuss an absolute version of this result.

Mathematics Subject Classification. Primary 14H30; Secondary 14H10, 14H25.
Key words and phrases. Anabelian open basis, generalized sub-$p$-adic field, hyperbolic polycurve, hyperbolic polycurve of strictly decreasing type.

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