In mathematics, Serre's multiplicity conjectures, named after Jean-Pierre Serre, are certain problems in commutative algebra, motivated by the needs of...

of linear algebraic groups Serre's modularity conjecture, concerning Galois representations Serre's multiplicity conjectures in commutative algebra Ribet's...

modularity conjecture Serre's multiplicity conjectures Serre's open image theorem Serre's property FA Serre relations Serre subcategory Serre functor Serre spectral...

square given by these maps commutes. Serre's Conjecture on Multiplicities. (cf. Serre's multiplicity conjectures.) Suppose that R is regular of dimension...

This is a list of notable mathematical conjectures. The following conjectures remain open. The (incomplete) column "cites" lists the number of results...

Tor's vanish, hence the multiplicity is positive. The positivity in the arbitrary case is one of Serre's multiplicity conjectures. The definition can be...

provided the tools for the eventual proof of the Weil conjectures by Pierre Deligne. From 1959 onward Serre's interests turned towards group theory, number theory...

Combinatorial commutative algebra Invariant theory Serre's multiplicity conjectures Homological conjectures Commutative ring Module (mathematics) Ring ideal...

d=\dim A} , the Krull dimension. See also: Serre's inequality on height and Serre's multiplicity conjectures. Regular local rings were originally defined...

from the Weil conjectures, except for the case k = 1, where it is a result of Deligne & Serre (1974). The Ramanujan–Petersson conjecture for Maass forms...

ring Intersection theory Weierstrass factorization theorem Serre's multiplicity conjectures Hilbert scheme - can be used to study modules on a scheme with...

intersection#Proper intersection. Serre gives the following proof of the inequality, based on the validity of Serre's multiplicity conjectures for formal power series...

Intersection theory Intersection number Chow ring Chern class Serre's multiplicity conjectures Albanese variety Picard group Modular form Moduli space Modular...

allowing physics to form a bridge between two mathematical areas. The conjectures made by Conway and Norton were proven by Richard Borcherds for the moonshine...

rows are B i {\displaystyle B_{i}} and whose columns are also bases. Serre's conjecture II: if G {\displaystyle G} is a simply connected semisimple algebraic...

research. The Artin conjecture for odd, irreducible, two-dimensional representations follows from the proof of Serre's modularity conjecture, regardless of...

47–87, MR 0088511 Serre, Jean-Pierre (1969–1970), "Facteurs locaux des fonctions zeta des varietés algébriques (définitions et conjectures)", Séminaire Delange-Pisot-Poitou...

example generalising the 1-dimensional "interval of groups" discussed in Serre's lectures on trees, where amalgamated free products are studied in terms...

Claude Chevalley, Masayoshi Nagata and Jean-Pierre Serre, motivated in part by the Weil conjectures relating number theory and algebraic geometry, further...

\lambda _{n}} . (Here it is understood that an eigenvalue with algebraic multiplicity μ occurs μ times in this list.) Then, it turns out the determinant of...

ISBN 978-0-387-94268-1, MR 1322960 Hochster, Melvin (2007), "Homological conjectures, old and new", Illinois J. Math., 51 (1): 151–169, doi:10.1215/ijm/1258735330...

the sum of the eigenvalues of ρ ( s ) {\displaystyle \rho (s)} with multiplicity. If the degree of the representation is n, then the sum is n long. If...

unitary operators and (2) each irreducible representation of K has finite multiplicity. alternating The alternating square of a representation V is a subrepresentation...