Linear patterns of prime elements in number fields

We prove that the von Mangoldt function $\Lambda _K$ of a number field $K$ is well approximated by its Cramer/Siegel models in the Gowers norm sense. Via the inverse theory of Gowers norms, this is achieved by showing that the difference of $\Lambda _K$ and its model is asymptotically orthogonal to nilsequences. To prove the asymptotic orthogonality, we use Mitsui's Prime Number Theorem as the base case and proceed by upgrading Green--Tao's type I/II sum computation to the general number field. As an application, we prove a number field analog of the Green--Tao--Ziegler theorem on simultaneous prime values of affine-linear forms of finite complexity.Comment: 94 page

Torsion and divisibility for reciprocity sheaves and 0-cycles with modulus

The notion of modulus is a striking feature of Rosenlicht-Serre's theory of generalized Jacobian varieties of curves. It was carried over to algebraic cycles on general varieties by Bloch-Esnault, Park, R\"ulling, Krishna-Levine. Recently, Kerz-Saito introduced a notion of Chow group of $0$-cycles with modulus in connection with geometric class field theory with wild ramification for varieties over finite fields. We study the non-homotopy invariant part of the Chow group of $0$-cycles with modulus and show their torsion and divisibility properties. Modulus is being brought to sheaf theory by Kahn-Saito-Yamazaki in their attempt to construct a generalization of Voevodsky-Suslin-Friedlander's theory of homotopy invariant presheaves with transfers. We prove parallel results about torsion and divisibility properties for them.Comment: 15 pages, exposition improve

モジュラス付き代数的サイクルの移動補題と反変性

学位の種別: 課程博士審査委員会委員 : （主査）東京大学教授 寺杣 友秀, 東京大学教授 斎藤 毅, 東京大学教授 辻 雄, 東京大学教授 志甫 淳, 東京大学准教授 三枝 洋一, 東京工業大学教授 齋藤 秀司University of Tokyo(東京大学

Started Activities of 80-Year-Old Japanese Seniors

18th ISA World Congress of Sociolog

Efficacy of Brazilian Propolis against Herpes Simplex Virus Type 1 Infection in Mice and Their Modes of Antiherpetic Efficacies

Ethanol extracts (AF-06, 07, and 08, 10 mg/kg) of Brazilian propolis were administered orally to cutaneously herpes simplex virus type 1 (HSV-1)-infected mice three times daily on days 0 to 6 after infection to evaluate their efficacies against HSV-1 infection and significantly limited development of herpetic skin lesions. AF-07 and 08 significantly reduced virus titers in brain and/or skin on day 4 without toxicity, but AF-08 had no anti-HSV-1 activity in vitro. AF-06 and 08 significantly enhanced delayed-type hypersensitivity (DTH) to inactivated HSV-1 antigen in infected mice. Oral AF-08-administration significantly augmented interferon (IFN)-γ production by HSV-1 antigen from splenocytes of HSV-1-infected mice, while direct exposure of splenocytes of infected mice to AF-06 significantly elevated IFN-γ production in vitro. Thus, AF-08 might have components that are active in vivo even after oral administration and those of AF-06 might be active only in vitro. Because DTH is a major host defense for intradermal HSV-1 infection, augmentation of DTH response by AF-06 or 08, directly or indirectly, respectively, may contribute to their efficacies against HSV-1 infection. In addition, AF-06 and 07 possibly contain anti-HSV-1 components contributing to their efficacies. Such biological activities of Brazilian propolis may be useful to analyze its pharmacological actions