Related papers: An arithmetic Riemann-Roch theorem in higher degre…

We apply techniques from symplectic geometry to extend and give a new proof of the complex convexity theorem of Gindikin-Kroetz.

An technically interesting proof of a known theorem.

We will present a new proof of the Gromoll-Grove diameter rigidity theorem.

In this article, we consider an analogue of Arakelov theory of arithmetic surfaces over a trivially valued field. In particular, we establish an arithmetic Hilbert-Samuel theorem and studies the effectivity up to R-linear equivalence of…

We prove a uniformization theorem in complex algebraic geometry.

This paper aims to give an elementary proof for Toponogov's theorem in Alexandrov geometry with lower curvature bound. The idea of the proof comes from the fact that, in Riemannian geometry, sectional curvature can be embodied in the second…

We derive explicit formulas for the Arakelov-Green function and the Faltings delta-invariant of a Riemann surface. A numerical example illustrates how these formulas can be used to calculate Arakelov invariants of curves.

In this paper we give a proof of an index theorem by Bismut. As a consequence we obtain another proof of the Grothendieck-Riemann-Roch theorem in differential cohomology.

We shall give a refinement of the arithmetic-geometric mean inequality.

We prove a generalisation of the Grothendieck-Riemann-Roch theorem, which is valid for any proper and flat morphism between noetherian and separated schemes of odd characteristic.

The classical arithmetic Grothendieck-Riemann-Roch theorem can be applied only to projective morphisms that are smooth over the complex numbers. In this paper we generalize the arithmetic Grothendieck-Riemann-Roch theorem to the case of…

We prove an analogue of the prime number theorem for finite fields.

In this paper, we will prove an analogue of Fujita's approximation theorem under the framework of Arakelov theory over adelic curves, which proves a conjecture of Huayi Chen and Atsushi Moriwaki.

We prove a mixed curvature analogue of Gromov's almost flat manifolds theorem for upper sectional and lower Bakry-Emery Ricci curvature bounds.

We prove an equivariant Riemann-Roch formula for divisors on algebraic curves over perfect fields. By reduction to the known case of curves over algebraically closed fields, we first show a preliminary formula with coefficients in Q. We…

We work with completed adelic structures on an arithmetic surface and justify that the construction under consideration is compatible with Arakelov geometry. The ring of completed adeles is algebraically and topologically self-dual and…

By some result on the study of arithemtic over trivially valued field, we find its applications to Arakelov geometry over adelic curves. We prove a partial result of the continuity of arithmetic $\chi$-volume along semiample divisors.…

We show a Riemann-Roch theorem for group ring bundles over an arithmetic surface; this is expressed using the higher adeles of Beilinson-Parshin and the tame symbol via a theory of adelic equivariant Chow groups and Chern classes. The…

In this paper we prove a concentration theorem for arithmetic $K_0$-theory, this theorem can be viewed as an analog of R. Thomason's result in the arithmetic case. We will use this arithmetic concentration theorem to prove a relative fixed…

It is well-known that a finite graph can be viewed, in many respects, as a discrete analogue of a Riemann surface. In this paper, we pursue this analogy further in the context of linear equivalence of divisors. In particular, we formulate…