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...

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...

height Serre group Serre's modularity conjecture Serre's multiplicity conjectures Serre's open image theorem Serre's property FA Serre relations Serre subcategory...

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

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...

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

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...

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...

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...

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

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

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...

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

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

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...

include: List of algebras List of algorithms List of axioms List of conjectures List of data structures List of derivatives and integrals in alternative...

\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...

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...

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...

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