This paper generalizes Yu. Manin’s approach toward a geometrical interpretation of Arakelov theory at infinity to linear cycles in projective spaces. We show how to interpret certain non-Archimedean Arakelov intersection numbers of linear cycles on Pn−1 with the combinatorial geometry of the Bruhat-Tits building associated to PGL(n). This geometric setting has an Archimedean analogue, namely, t...

The aim of the present paper is to introduce the concept of joint common limit range property ((JCLR) property) for single-valued and set-valued maps in non-Archimedean fuzzy metric spaces. We also list some examples to show the difference between (CLR) property and (JCLR) property. Further, we establish common fixed point theorems using implicit relation with integral contractive condition. Se...

We develop the theory of pinchings for non-archimedean analytic spaces. In particular, we show that although affinoid spaces do not have to be affinoid, Hausdorff always exist in category

We determine some stability results concerning the pexiderized quadratic functional equation in non-Archimedean fuzzy normed spaces. Our result can be regarded as a generalization of the stability phenomenon in the framework of L-fuzzy normed spaces. AMS Mathematics Subject Classification (2010): 00A11; Primary 46S40; Secondary 39B52, 39B82, 26E50, 46S50.

We introduce the notion of the Gromov-Hausdorff fuzzy distance between two non-Archimedean fuzzy metric spaces (in the sense of Kramosil and Michalek). Basic properties involving convergence and the fuzzy version of the completeness theorem are presented. We show that the topological properties induced by the classic Gromov-Hausdorff distance on metric spaces can be deduced from our approach.

In this paper, we prove the generalized Hyers-Ulam stability of the quadratic functional equation f(x+ y) + f(x− y) = 2f(x) + 2f(y) in non-Archimedean L-fuzzy normed spaces.

The discrete Lotka–Volterra equation over p-adic space was constructed since p-adic space is a prototype of spaces with non-Archimedean valuations and the space given by taking the ultra-discrete limit studied in soliton theory should be regarded as a space with the non-Archimedean valuations given in my previous paper (Matsutani S 2001 Int. J. Math. Math. Sci.). In this paper, using the natura...

We prove that if X,X are closed subschemes of a torus T over a non-Archimedean field K, of complementary codimension and with finite intersection, then the stable tropical intersection along a (possibly positive-dimensional, possibly unbounded) connected componentC of Trop(X)∩Trop(X) lifts to algebraic intersection points, with multiplicities. This theorem requires potentially passing to a suit...