In algebraic geometry, the Serre–Tate theorem says that an abelian scheme and its p-divisible group have the same infinitesimal deformation theory. This...

subcategory Serre functor Serre spectral sequence Lyndon–Hochschild–Serre spectral sequence Serre–Swan theorem Serre–Tate theorem Serre's theorem in group...

p-divisible (Tate–Barsotti) groups. Many of his results were not immediately published and some of them were written up by Serge Lang, Jean-Pierre Serre, Joseph...

variety, the theorem says that a cohomology group H i {\displaystyle H^{i}} is the dual space of another one, H n − i {\displaystyle H^{n-i}} . Serre duality...

p-adic modular form; and the Serre conjecture (now a theorem) on mod-p representations that made Fermat's Last Theorem a connected part of mainstream...

Jean-Pierre Serre and proven by Ken Ribet. The proof was a significant step towards the proof of Fermat's Last Theorem (FLT). As shown by Serre and Ribet...

Jean-Pierre Serre, who proved all but one part known as the "epsilon conjecture" (see: Ribet's Theorem and Frey curve). These papers by Frey, Serre and Ribet...

}({\sqrt {-3}},{\sqrt {13}})/{\mathbf {Q} }} but is not a global norm. Serre and Tate showed that another counterexample is given by the field Q ( 13 , 17...

completed in 1987 when Jean-Pierre Serre identified a missing link (now known as the epsilon conjecture or Ribet's theorem) in Frey's original work, followed...

model, potential good reduction, Tate curve, semistable abelian variety, semistable elliptic curve, Serre–Tate theorem. Grothendieck–Katz conjecture The...

groups, Dieudonné theory, and Galois representations. For example, the Serre-Tate theorem implies that the deformations of a group scheme are strongly controlled...

(2024-09-01). "THE SELMER GROUP, THE SHAFAREVICH-TATE GROUP, AND THE WEAK MORDELL-WEIL THEOREM" (PDF). Tate 1963. Swinnerton-Dyer 1967. Poonen & Stoll 1999...

p-divisible group. Deformations of abelian schemes are, according to the Serre–Tate theorem, governed by the deformation properties of the associated p-divisible...

numbers. Mumford (1966) introduced Mumford–Tate groups over the complex numbers under the name of Hodge groups. Serre (1967) introduced the p-adic analogue...

})} giving a curve over Z p {\displaystyle \mathbb {Z} _{p}} . The Serre–Tate theorem asserts, roughly speaking, that the deformations of abelian scheme...

higher cohomology groups vanish. Tate duality, a global version (i.e. for global fields) Serre 2002, Theorem II.5.2 Serre 2002, §II.4.3 Some authors use...

develops a new theory of the equations defining abelian varieties 1968 Serre–Tate theorem on good reduction extends the results of Max Deuring on elliptic curves...

Klein's dessins d'enfant and the buckyball. Serre, Jean-Pierre (1997). Lectures on the Mordell-Weil theorem. Aspects of Mathematics. Vol. 15. Translated...

character is in I(G). Several proofs of the theorem, beginning with a proof due to Brauer and John Tate, show that the trivial character is in the analogously...

Grothendieck's theorem shows that the higher direct images of coherent sheaves under a proper map are coherent; this reduces to Serre's theorem over a one-point...

JFM 61.1043.02, Zbl 0011.14601 Serre, Jean-Pierre (1973), A course in arithmetic, pp. 5–6, ISBN 0-387-90040-3 "Proofs of the Chevalley-Warning theorem"....

The composition series in the Jordan–Hölder theorem is a non-abelian generalization. Silverman & Tate (1992), p. 102 de la Harpe (2000), p. 46 Fuchs...

Mathematicians in Nice (The regularity theorem in algebraic geometry) and in 1978 in Helsinki (p-adic L functions, Serre-Tate local moduli and ratios of solutions...

Tate 2009, corollary to theorem XI.14, p. 100 As in Serre 1967, §4.2 Serre 1967, §2.5, proposition 4 Milne 2008, theorem III.3.5 As in Artin & Tate 2009...

subgroup". In Linear Representation of Finite Groups Serre states in Chapter 9.2, 17 the theorem in the following, more general way: Let G {\displaystyle...

Vojta wrote: While others at the time shared this viewpoint (e.g., Weil, Tate, Serre), it is easy to forget that others did not, as Mordell's review of Diophantine...

Farb & Dennis 1993, Proposition 4.16 Serre 1979, p. 162 Gille & Szamuely 2006, Theorem 6.2.8 Serre 1979, p. 163 Serre 1979, p. 193 Gille & Szamuely 2006...

the principal ideal theorem in class field theory. See the Emil Artin-John Tate Class Field Theory notes. Focal subgroup theorem, an important application...

established by Emil Artin in a series of papers (1924; 1927; 1930), is a general theorem in number theory that forms a central part of global class field theory...

Last Theorem. In 1986, Ribet proved that the epsilon conjecture formulated by Jean-Pierre Serre was true, and thereby proved that Fermat's Last Theorem would...