result in arithmetic geometry
C24993
concept
A result in arithmetic geometry is a theorem or proposition that connects number-theoretic properties of solutions to polynomial equations with the geometric structure of the varieties they define over arithmetic fields.
Observed surface forms (9)
| Surface form | Occurrences |
|---|---|
| result in algebraic number theory | 3 |
| theorem in arithmetic geometry | 3 |
| result in Galois cohomology | 2 |
| Riemann–Roch type theorem | 1 |
| Weil–Tate pairing | 1 |
| result in Diophantine geometry | 1 |
| result in p-adic analysis | 1 |
| set of formulas in algebraic geometry | 1 |
| statement in arithmetic geometry | 1 |
Instances (17)
| Instance | Via concept surface |
|---|---|
| Hasse bound for elliptic curves | — |
| Hasse norm theorem | result in algebraic number theory |
| Weil conjectures | — |
| Grothendieck–Riemann–Roch theorem | Riemann–Roch type theorem |
| Grothendieck–Ogg–Shafarevich formula | — |
| Plücker formulas | set of formulas in algebraic geometry |
| Kummer congruences | result in algebraic number theory |
| Hensel’s lemma | result in p-adic analysis |
| Faltings' theorem | theorem in arithmetic geometry |
| cubic reciprocity law | result in algebraic number theory |
| Sato–Tate distribution (for families of elliptic curves) | theorem in arithmetic geometry |
| Hasse–Weil bound for abelian varieties | theorem in arithmetic geometry |
| Siegel's theorem on integral points | result in Diophantine geometry |
| proof of the Milnor conjecture | result in Galois cohomology |
| Tate pairing | Weil–Tate pairing |
| Poitou–Tate duality | result in Galois cohomology |
| Bloch–Kato conjecture | statement in arithmetic geometry |