5 papers
Symmetries of spaces and numbers -- anabelian geometry
Benjamin Collas, Takahiro Murotani, Naganori Yamaguchi
``Can number and geometric spaces be reconstructed from their symmetries?'' This question, which is at the heart of anabelian geometry, a theory built on the collaborative efforts…
Anabelian properties of tame fundamental groups of singular curves
Takahiro Murotani
In anabelian geometry, we consider to what extent the étale or tame fundamental groups of schemes reflect geometric properties of the schemes. Although there are many known results…
Some Kummer extensions over maximal cyclotomic fields, a finiteness theorem of Ribet and TKND-AVKF fields
Takahiro Murotani, Yoshiyasu Ozeki
It is a theorem of Ribet that an abelian variety defined over a number field has only finitely many torsion points with values in the maximal cyclotomic extension field $K^{\ma…
Anabelian properties of infinite algebraic extensions of finite fields
Takahiro Murotani
The Grothendieck conjecture for hyperbolic curves over finite fields was solved affirmatively by Tamagawa and Mochizuki. On the other hand, (a ``weak version'' of) the Grothendieck…
Geometric properties of homomorphisms between the absolute Galois groups of mixed-characteristic complete discrete valuation fields with perfect residue fields
Takahiro Murotani
Although the analogue of the theorem of Neukirch-Uchida for -adic local fields fails to hold as it is, Mochizuki proved a certain analogue of this theorem for the absolute Galoi…