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Quantum arithmetic of Drinfeld modules

Igor V. Nikolaev

Abstract

We study the quantum invariants of projective varieties over the number fields. Namely, explicit formulas for a functor $\mathscr{Q}$ on such varieties are proved. The case of abelian varieties with complex multiplication is treated in detail.

Quantum arithmetic of Drinfeld modules

Abstract

We study the quantum invariants of projective varieties over the number fields. Namely, explicit formulas for a functor on such varieties are proved. The case of abelian varieties with complex multiplication is treated in detail.

Paper Structure

This paper contains 10 sections, 10 theorems, 14 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Noncommutative geometry
  4. $C^*$-algebras
  5. K-theory of $C^*$-algebras
  6. Noncommutative tori
  7. Non-abelian class field theory
  8. Quantum arithmetic
  9. Proof of Theorem \ref{['thm1.1']}
  10. Complex multiplication

Key Result

Theorem 1.1

Figures (1)

  • Figure 1: Handelman's triples

Theorems & Definitions (19)

  • Theorem 1.1
  • Theorem 2.1
  • Corollary 2.2
  • Definition 2.3
  • Example 2.4
  • Theorem 2.5
  • Lemma 3.1
  • proof
  • Corollary 3.2
  • proof
  • ...and 9 more