1 citations · 2 across the 7 of their papers we have counts for
7 papers
Minimal log regular models of hyperbolic curves over discrete valuation fields
Ippei Nagamachi
In the famous paper of Deligne and Mumford, they proved that a proper hyperbolic curve over a discrete valuation field has stable reduction if and only if the Jacobian variety of t…
On behavior of conductors, Picard schemes, and Jacobian numbers of varieties over imperfect fields
Ippei Nagamachi, Teppei Takamatsu
Let be a regular geometrically integral variety over an imperfect field . Unlike the case of characteristic , may have s…
The Shafarevich conjecture and some extension theorems for proper hyperbolic polycurves
Ippei Nagamachi, Teppei Takamatsu
In this paper, we prove the Shafarevich conjecture for proper hyperbolic polycurves, which is a higher dimensional analogue of that for proper hyperbolic curves. First, we study th…
Topics in the Grothendieck conjecture for hyperbolic polycurves of dimension 2
Ippei Nagamachi
In this paper, we study the anabelian geometry of hyperbolic polycurves of dimension 2 over sub-p-adic fields. In 1-dimensional case, Mochizuki proved the Hom version of the Grothe…
On homotopy exact sequences for normal schemes
Ippei Nagamachi
Consider a morphism between connected locally Noetherian normal schemes. In this paper, we discuss when the sequence of the etale fundamental groups associated to the morphism is e…
Criteria for good reduction of proper polycurves
Ippei Nagamachi
We give good reduction criteria for hyperbolic polycurves, i.e., successive extensions of families of curves, under mild assumption. These criteria are higher dimensional version o…
On a good reduction criterion for proper polycurves with sections
Ippei Nagamachi
We give a good reduction criterion for proper polycurves with sections,i.e., successive extensions of family of curves with section, under mild assumption. This criterion is a high…