Algebra — Open Conjectures
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Includes conjectures from algebraic geometry, algebraic topology, algebraic K-theory, commutative algebra, ring theory, group theory, and algebraic curves.
Algebraic Geometry
| # | Conjecture | Eponym(s) | Comments |
|---|---|---|---|
| 1 | Hodge conjecture | W. V. D. Hodge | |
| 2 | MNOP conjecture | — | |
| 3 | Standard conjectures on algebraic cycles | — | |
| 4 | Tate conjecture | John Tate | |
| 5 | Virasoro conjecture | Miguel Ángel Virasoro | |
| 6 | Weight monodromy conjecture | — |
Algebraic Topology
| # | Conjecture | Eponym(s) | Comments |
|---|---|---|---|
| 1 | Eilenberg–Ganea conjecture | Samuel Eilenberg, Tudor Ganea | |
| 2 | Novikov conjecture | Sergei Novikov | |
| 3 | Whitehead conjecture | J. H. C. Whitehead |
Algebraic K-theory
| # | Conjecture | Eponym(s) | Comments |
|---|---|---|---|
| 1 | Bloch–Kato conjecture | Spencer Bloch, Kazuya Kato |
Commutative Algebra
| # | Conjecture | Eponym(s) | Comments |
|---|---|---|---|
| 1 | Homological conjectures in commutative algebra | — | |
| 2 | Serre’s multiplicity conjectures | Jean-Pierre Serre |
Ring Theory
| # | Conjecture | Eponym(s) | Comments |
|---|---|---|---|
| 1 | Jacobson’s conjecture | Nathan Jacobson | |
| 2 | Kaplansky conjectures | Irving Kaplansky | |
| 3 | Köthe conjecture | Gottfried Köthe |
Group Theory
| # | Conjecture | Eponym(s) | Comments |
|---|---|---|---|
| 1 | Andrews–Curtis conjecture | James J. Andrews, Morton L. Curtis | Combinatorial group theory |
| 2 | Cherlin–Zilber conjecture | Gregory Cherlin, Boris Zilber | |
| 3 | Herzog–Schönheim conjecture | Marcel Herzog, Jochanan Schönheim |
Algebraic Curves
| # | Conjecture | Eponym(s) | Comments |
|---|---|---|---|
| 1 | Green’s conjecture | Mark Lee Green |