Number fields and function fields: two parallel worlds

By Gerard van der Geer, B. Moonen, R. Schoof. 2005

152 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/46dd4015f6720519485bfec9c5a080bd459d1f23

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Tamás Hausel
2. Fernando Rodriguez-Villegas

In Geometry and Topology

1. Tamás Hausel
2. Fernando Rodriguez-Villegas
3. O. Schiffmann
4. Anton Mellit
5. M. A. Cataldo
6. O. Garc'ia-Prada
7. V. Muñoz
8. Sam Payne

In Mathematical Physics

1. Tamás Hausel
2. Fernando Rodriguez-Villegas
3. O. Schiffmann
4. Anton Mellit
5. M. A. Cataldo
6. O. Garc'ia-Prada
7. V. Muñoz
8. Sam Payne

Citations in the corpus

• F1-schemes and toric varieties (2006, unknown): “In [10] the authors formalize the transition from rings to schemes on a categorial level and apply this machinery to the category of sets to obtain the category of F1-schemes as in [1].”
• Mixed Hodge polynomials of character varieties (2006, background): “1A similar property for smooth and proper schemes was studied in [13].”
• Mapping F_1-land:An overview of geometries over the field with one element (2009, unknown): “…s 2 )ζ(s) = det∞ ( 1 2π (s− Θ) ∣∣∣H1(Spec Z,OT ) ) det∞ ( 1 2π (s− Θ) ∣∣∣H0(Spec Z,OT ) ) det∞ ( 1 2π (s− Θ) ∣∣∣H2(Spec Z,OT ) ) wheredet∞ denotes the regularized determinant,Θ is an endofunctor that comes with the category of motives andHi(Spec Z,OT ) are certain proposed cohomology groups.”