On the Injectivity of the Homomorphisms from the Automorphism Groups of Fields to the Outer Automorphism Groups of the Absolute Galois Groups

In the present paper, we discuss the injectivity of the natural homomorphism from the automorphism group of a given field to the outer automorphism group of the associated absolute Galois group. We prove that this natural homomorphism is injective in the case where, for instance, the given field may be embedded into the field of fractions of some Noetherian local domain of mixed characteristic

Construction of Abundant Explicit Nongeometric Pro-p Galois Sections of Punctured Projective Lines

In the present paper, we construct abundant explicit nongeometric pro-p Galois sections of certain punctured projective lines. Moreover, we also obtain an application to the theory of Massey products

A Note on Stable Reduction of Smooth Curves Whose Jacobians Admit Stable Reduction

P. Deligne and D. Mumford proved that, for a smooth curve over the field of fractions of a discrete valuation ring whose residue field is perfect, if the associated Jacobian has stable reduction over the discrete valuation ring, then the smooth curve has stable reduction over the discrete valuation ring. Recently, I. Nagamachi proved a similar result over a connected normal Noetherian scheme of dimension one. In the present paper, we prove a similar result over a Prüfer domain, i.e., a domain whose localization at each of the prime ideals is a valuation ring. Moreover, we also give a counter-example in a situation over a higher dimensional base case. More precisely, we construct an example of a smooth curve over the field of fractions of a complete strictly Henselian normal Noetherian local domain of equal characteristic zero such that the associated Jacobian has good reduction over the local domain, but the smooth curve does not have stable reduction over the local domain

The Anabelian Geometry of Configuration Spaces of Hyperbolic Curves in Positive Characteristic

In the present paper, we prove the anabelian Grothendieck conjecture for the tame fundamental groups of the configuration spaces associated to hyperbolic curves over [the perfections of] finitely generated fields of positive characteristic. The main theorem of the present paper generalizes the classical anabelian results for hyperbolic curves in positive characteristic established by A. Tamagawa, S. Mochizuki, and J. Stix. The main theorem of the present paper may also be regarded as the first anabelian Grothendieck conjecture-type result for algebraic varieties in positive characteristic of higher dimension [i.e., of dimension greater than one]. In the process of the proof of the main theorem, we prove a certain exactness of homotopy sequences for the tame fundamental groups with respect to suitable morphisms between normal varieties. Moreover, we also introduce the notion of a generalized fiber subgroup of the tame fundamental group of the configuration space associated to a hyperbolic curve in arbitrary characteristic and establish a “group-theoretic algorithm” that reconstructs, from the tame fundamental group of the configuration space, the generalized fiber subgroups

Combinatorial Construction of the Absolute Galois Group of the Field of Rational Numbers

In this paper, we give a purely combinatorial/group-theoretic construction of the conjugacy class of subgroups of the Grothendieck-Teichmüller group GT determined by the absolute Galois group GQ def = Gal(Q/Q) [where Q denotes the field of algebraic numbers] of the field of rational numbers Q. In fact, this construction also yields, as a by-product, a purely combinatorial/group-theoretic characterization of the GT-conjugates of closed subgroups of GQ that are "sufficiently large" in a certain sense. We then introduce the notions of TKND-fields [i.e., "torally Kummernondegenerate fields"] and AVKF-fields [i.e., "abelian variety Kummerfaithful fields"], which generalize, respectively, the notions of "torally Kummer-faithful fields" and "Kummer-faithful fields" [notions that appear in previous work of Mochizuki]. For instance, if we write Qab⊆ Q for the maximal abelian extension field of Q, then every finite extension of Qab is a TKND-AVKF-field [i.e., both TKND and AVKF]. We then apply the purely combinatorial/group-theoretic characterization referred to above to prove that, if a subfield K ⊆ Q is TKND-AVKF, then the commensurator in GT of the subgroup GK⊆ GQ determined by K is contained in GQ. Finally, we combine this computation of the commensurator with a result of Hoshi-Minamide-Mochizuki concerning GT to prove a semi-absolute version of the Grothendieck Conjecture for higher dimensional [i.e., of dimension ≥ 2] configuration spaces associated to hyperbolic curves of genus zero over TKND-AVKF-fields

Characterization of a Radical <i>S</i>‑Adenosyl‑l‑methionine Epimerase, NeoN, in the Last Step of Neomycin B Biosynthesis

The last step of neo­mycin biosynthesis is the epimer­ization at C-5‴ of neo­mycin C to give neo­mycin B. A candidate enzyme responsible for the epimer­ization was a putative radical <i>S</i>-adenosyl-l-methionine (SAM) enzyme, NeoN, which is uniquely encoded in the neo­mycin biosynthetic gene cluster and remained an unassigned protein in the neo­mycin biosynthesis. The reconstituted and reduced NeoN showed the expected epimer­ization activity in the presence of SAM. In the epimer­ization, 1 equiv of SAM was consumed to convert neo­mycin C into neo­mycin B. The site of neo­mycin C reactive toward epimer­ization was clearly confirmed to be C-5‴ by detecting the incorporation of a deuterium atom from the deuterium oxide-based buffer solution. Further, alanine scanning of the NeoN cysteine residues revealed that C249 is a critical amino acid residue that provides a hydrogen atom to complete the epimer­ization. Furthermore, electron paramagnetic resonance analysis of the C249A variant in the presence of SAM and neo­mycin C revealed that a radical intermediate is generated at the C-5‴ of neo­mycin C. Therefore, the present study clearly illustrates that the epimer­ization of neo­mycin C to neo­mycin B is catalyzed by a unique radical SAM epimerase NeoN with a radical reaction mechanism

Alzheimer Aβ Assemblies Accumulate in Excitatory Neurons upon Proteasome Inhibition and Kill Nearby NAKα3 Neurons by Secretion

アルツハイマー病の神経毒性物質の形成と伝搬機構を解明 --発症に繋がる新たなメカニズムを提案--. 京都大学プレスリリース. 2019-03-01.We identified ∼30-mer amyloid-β protein (Aβ) assemblies, termed amylospheroids, from brains of patients with Alzheimer disease (AD) as toxic entities responsible for neurodegeneration and showed that Na+, K+-ATPase α3 (NAKα3) is the sole target of amylospheroid-mediated neurodegeneration. However, it remains unclear where in neurons amylospheroids form and how they reach their targets to induce neurodegeneration. Here, we present an in vitro culture system designed to chronologically follow amylospheroid formation in mature neurons expressing amyloid precursor protein bearing early-onset AD mutations. Amylospheroids were found to accumulate mainly in the trans-Golgi network of excitatory neurons and were initially transported in axons. Proteasome inhibition dramatically increased amylospheroid amounts in trans-Golgi by increasing Aβ levels and induced dendritic transport. Amylospheroids were secreted and caused the degeneration of adjacent NAKα3-expressing neurons. Interestingly, the ASPD-producing neurons later died non-apoptotically. Our findings demonstrate a link between ASPD levels and proteasome function, which may have important implications for AD pathophysiology