Yu YANG@RIMS, Kyoto University
Homepage of Yu YANG
Project Assistant Professor
Research Institute for Mathematical Sciences, Kyoto University
Kyoto 606-8502, Japan
e-mail: yuyang(at)kurims.kyoto-u.ac.jp
- Publications/Preprints
- Talks
- Conferences/Visitor Seminar
- Žö‹Æ
- About Me
Publications
Topology of moduli spaces of curves and anabelian geometry in positive characteristic (with Z. Hu, R. Zong), [pdf], arXiv.
Forum of Mathematics, Sigma 12 (2024), Paper No. e33, 36 pp.
Towards Grothendieck's anabelian dream for curves over algebraically closed fields of characteristic p.
Oberwolfach Rep. 42 (2023).
p-groups, p-rank, and semi-stable reduction of coverings of curves, [pdf].
Algebra & Number Theory 18 (2024), No.2, 281-317.
On topological and combinatorial structures of pointed stable curves over algebraically closed fields of positive characteristic, [pdf].
Math. Nachr. (2023), 1-42.
Maximum generalized Hasse-Witt invariants and their applications to anabelian geometry, [pdf].
Selecta Math. (N.S.) 28 (2022), Paper No. 5, 98 pp.
View-only version of Springer Nature Content Sharing Initiative
Raynaud-Tamagawa theta divisors and new-ordinariness of ramified coverings of curves, [pdf].
J. Algebra 587 (2021), 263-294.
On the existence of specialization isomorphisms of admissible fundamental groups in positive characteristic, [pdf].
Math. Res. Lett. 28 (2021), 1941-1959.
On the averages of generalized Hasse-Witt invariants of pointed stable curves in positive characteristic, [pdf].
Math. Z. 295 (2020), 1-45.
The anabelian geometry of curves over algebraically closed fields of positive characteristic, [pdf].
RIMS Kokyuroku Bessatsu B83 (2020), 47-58.
Group-theoretic characterizations of almost open immersions of curves, [pdf].
J. Algebra 530 (2019), 290-325.
On the admissible fundamental groups of curves over algebraically closed fields of characteristic p>0, [pdf].
Publ. Res. Inst. Math. Sci. 54 (2018), 649-678.
On the existence, geometry and p-ranks of vertical fibers of coverings of curves, [pdf].
RIMS Kokyuroku Bessatsu B72 (2018), 187-193.
On the ordinariness of coverings of stable curves, [pdf].
C. R. Math. Acad. Sci. Paris, Ser. I 356 (2018), 17-26.
On the existence of non-finite coverings of stable curves over complete discrete valuation rings, [pdf].
Math. J. Okayama Univ. 61 (2019), 1-18.
Degeneration of period matrices of stable curves, [pdf].
Kodai Math. J. 41 (2018), 125-153.
Preprints
On the generalized essential dimension conjecture II: The case of closed points of hyperelliptic locus of $M_{3}$, [pdf].
On the generalized essential dimension conjecture I: The case of closed points of $\overline M_{1, r}$ and $\overline M_{2}$, [pdf].
In this series of papers, we study the so-called "generalized essential dimension conjecture" (=GEDC), which was formulated by myself in the paper "Moduli spaces of fundamental groups of curves in positive characteristic I", and which was formulated by using the philosophy of moduli spaces of fundamental groups. This conjecture is a generalization of Tamagawa's essential dimension conjecture (=EDC), the latter is a significant extension of his famous finiteness theorem. Since Tamagawa formulated his conjecture in 1999, very few results (i.e., closed points for $M_{0,n}$ and $M_{1,1}$) have been known for the EDC over the past 25 years. The main results of the series of papers show that the "GEDC" holds for closed points of $\overline M_{0, n}$, $\overline M_{1, n}$, $\overline M_{2}$, and the hyperelliptic locus $H_{3}$.
Generalized Hasse-Witt invariants for coverings with prescribed ramifications, [pdf].
On finite quotients of tame fundamental groups of curves in positive characteristic, [pdf].
In the present paper, we give an explicit construction of differences of tame fundamental groups of certain non-isomorphic curves via finite quotients. In particular, our construction shows that the anabelian phenomena for curves over algebraically closed fields of positive characteristic can be understood by using not only entire tame fundamental groups but also certain finite quotients of them.
On the arithmetic fundamental groups of curves over local fields (with Y. Hoshi), [pdf].
In the present paper, we establish a method to treat artithmetic fundamental groups of curves over both mixed characteristic and positive characteristic local fields. In particular, we obtain a new proof of Mochizuki's famous theorem concerning (Isom-version) Grothendieck's anabelian conjecture for curves over sub-p-adic fields without using p-adic Hodge theory.
On the averages of p-rank of generic curves in positive characteristic, [pdf].
Topological and group-theoretical specializations of fundamental groups of curves in positive characteristic, [pdf].
In the present paper, by using the philosophy of the theory of moduli spaces of fundamental groups, we formulate a new conjecture which I call the "group-theoretical specialization conjecture". This conjecture can be regarded as a topological and combinatorial version of the homeomorphism conjecture and is a main step toward the homeomorphism conjecture for higher dimensional moduli spaces. Moreover, it's the ultimate generalization of the so-called combinatorial Grothendieck conjecture in positive characteristic. The combinatorial Grothendieck conjecture is the main conjecture in the theory of combinatorial anabelian geometry which was developed by Y. Hoshi and S. Mochizuki in characteristic 0 and by A. Tamagawa and the author in positive characteristic.
Moduli spaces of fundamental groups of curves in positive characteristic I, [pdf], arXiv.
The moduli spaces of fundamental groups give a general formulation for describing anabelian phenomena of curves over algebraically closed fields of positive characteristics which were discovered by Prof. A. Tamagawa in 1996. In particular, the main conjecture of our theory (= the Homeomorphism Conjecture) supplies a viewpoint to see what properties of fundamental groups should be anabelian. See the talk slides 2021.6.30RIMS
and 2021.7.9RIMS (or the introduction of the paper)
for my considerations about this theory.
Moreover, since the theory of moduli spaces of fundamental groups was proposed in the summer of 2019, a series of significant advancements have been made by myself. However, due to numerous chores, I haven't had the time to write down some of these results yet. For important results up until the summer of 2023, see the video of my talk at the Oberwolfach-RIMS conference titled "Fundamental groups of curves in positive characteristic as local moduli".
visits to this page since August 12, 2017.