It states that every finitely generated projective module over a polynomial ring is free geometrically, finitely generated projective modules correspond to vector bundles over affine. Now we introduce some more symbols to state the conjecture we mentioned. My course was taught very much in the spirit of a mathematical guided tour. Volunteering as the guide, i took upon myself the task of charting a route. Serre conjecture states that all such representations come from modular forms, and then it takes only a bit of.
As serre explained in bordeaux, the conjecture predicts in fact that there are no. Conjectures definition of conjectures by the free dictionary. Conjectured definition of conjectured by the free dictionary. Not to be confused with the serre conjecture in number theory or the quillensuslin theorem, which is sometimes also referred to as serres conjecture in mathematics, jeanpierre serre conjectured the following statement regarding the galois cohomology of a simply connected semisimple algebraic group. Serre furthermore asked whether his conjecture could be rephrased in terms of a \mod langlands philosophy. Wiles, with the help of richard taylor, famously cracked the problem. Serres conjecture is in a sense a parent of fermats last theorem.
Synonyms for conjectures include guesses, surmises, fancies, speculations, notions, suppositions, theories, assumptions, hypotheses and inferences. We hope that the following list of synonyms for the word conjecture will help you to finish your crossword today. Khare settled the serre conjecture in the affirmative. I offered a course on serres conjecture to a small group of graduate students in january, 1977 at the university of california, berkeley one year after its solution by quillen and suslin. Brueggeman treated the case p 5 modulo the generalized riemann hypothesis. The conjecture was proved by chandrashekhar khare in the level 1 case, in 2005. The use of certain textual elements is assumed to be systematic. The naive definition of modular forms mod p that we are using following serre is not quite adequate in this context, and katzs definition of. In mathematics, serres modularity conjecture, introduced by jeanpierre serre 1975, 1987, states that an odd, irreducible, twodimensional galois representation over a finite field arises from a modular form. Conjecture definition, the formation or expression of an opinion or theory without sufficient evidence for proof. On serres conjecture for 2dimensional mod p representations of galq q by chandrashekhar khare and jeanpierre wintenberger abstract we prove the existence in many cases of minimally rami ed padic lifts of 2dimensional continuous, odd, absolutely irreducible, mod prepresentations.
Definition and synonyms of conjecture from the online english dictionary from macmillan education this is the british english definition of conjecture. Serre river, a tributary of the oise in france serre, campania, a town and comune in the province of salerno in the campania region. Se7, serre conjectures that the converse holds as well. Synonyms for conjectured at with free online thesaurus, antonyms, and definitions. Make conjectures crossword answers, clues, definition.
Serre in 1955, to the effect that one did not know if. Serres conjecture and base change for gl2 85 if there exists an embedding i. Ruinous synonyms best 52 synonyms for ruinous thesaurus. Conjecture the restoration of a part of a text that is unreadable or completely absent in the original manuscript, which a researcher introduces into a text in the course of a scholarly description. The quillensuslin theorem, also known as serre s problem or serre s conjecture, is a theorem in commutative algebra about the relationship between free modules and projective modules over polynomial rings. Serre chevalier, a major french ski resort in the southern part of the alps. In this paper serre outlined a conjecture detailing a precise relationship between certain mod p galois representations and speci. This paper is the first part of a work which proves serres modularity conjecture.
Assume now that we know serres conjecture mod p, and let p be as above i. If we look at data over the precipitation in a city for 29 out of 30 days and see that it has been raining every single day it would be a good guess that it will be raining the 30 th day as well. Representations arising from an elliptic curve 12 1. Long term outlook for the statutory pension insurance scheme.
Find 1590 synonyms for conjecture and other similar words that you can use instead based on 8 separate contexts from our thesaurus. Mathematicians choice of terminology for the conjecture largely broke down. The conjecture is strong enough to imply among other things, fermats last theorem, a problem that had remained unsolved for more than three hundred years until it was solved by andrew wiles a few years back. This statement was motivated by the fact that 1 n the af. For those values of p, there simply are no representations. The conjecture was proved by chandrashekhar khare in the level 1 case, in 2005 and later in. Partly in collaboration with wintenberger, professor chandrashekhar b. Conjecture article about conjecture by the free dictionary. Conjectures are ideas or notions founded on probabilities without any demonstration of their truth. G is called the characteristic map and the mapping.
Serre may refer to claude serre 19381998, a french cartoonist. Bas edixhoven september 23, 2005 abstract the conjecture will be stated, and put in its historical context and in the wider context of the langlands program. Conjectures as to napoleons awareness of the danger of extending his line, and on the russian side as to luring the enemy into the depths of russia, are evidently of that kind, and only by much straining can historians attribute such conceptions to napoleon and his marshals, or such plans to the russian commanders. View american english definition of conjecture change your default dictionary to american english. Given to, characterized by, or based upon speculation or conjecture. Then there exists a newform fwhose galois representation.
Emerton for his enlightening lecture on katzs definition of modular forms. Conjectures definition of conjectures by medical dictionary. If, on the other hand, a has good ordinary reduction, then a extends to an abelian scheme a over the ring of integers rv of kv. Lectures on serres conjectures 1 preface 2 chapter 1. Conjecture is a 10 letter word starting with c and ending with e synonyms, crossword answers and other related words for conjecture. Namely, he conjectured that if g is such a group over a perfect. A conjecture is an educated guess that is based on known information. Later, serre proved the conjecture for p 3 in a similar manner. Serres conjecture and more akshay october 9, 2009 notes by sam lichtenstein fix embeddings q. Synonyms for conjecture at with free online thesaurus, antonyms, and definitions. Conjecture synonyms, conjecture antonyms merriamwebster. The hard work is in formulating an analogue of the \weight part of serres conjecture. A statement or an idea which is unproven, but is thought to be true.
The zeta function of any elliptic curve with rational coefficients. Top antonyms for conjecture opposite of conjecture are fact, proof and interpret. The reconstruction of a text is based on historical, linguistic, and paleographic data. Conjecture meaning in the cambridge english dictionary. Antonyms for conjecture include fact, calculation, certainty, measurement, proof, reality, truth, knowledge, disbelief and information. Synonyms, crossword answers and other related words for make conjectures speculate we hope that the following list of synonyms for the word speculate will help you to finish your crossword today. Opinion or judgment based on inconclusive or incomplete evidence.
Serres conjecture, for the most part of the second half of the 20th century, ferred to the famous statement made by j. In some sense, this is an analogue of the shimurataniyama conjecture for mod p representations. Top synonym for conjecture another word for conjecture is guess. Conjecture definition of conjecture by merriamwebster. In mathematics, serre s modularity conjecture, introduced by jeanpierre serre 1975, 1987, states that an odd, irreducible, twodimensional galois representation over a finite field arises from a modular form. An irreducible automorphic representation is called ordinary at if it is generated by a hecke eigenform ordinary at. In mathematics, serres multiplicity conjectures, named after jeanpierre serre, are certain purely algebraic problems, in commutative algebra, motivated by the needs of algebraic geometry. Weve arranged the synonyms in length order so that they are easier to find. Serres modularity conjecture i chandrashekhar khare and jeanpierre wintenberger to jeanpierre serre abstract. Ifa has multiplicative reduction, the theory of the tate abelian variety yields an exact sequence 0.
This conjecture and its variants have become known as serres conjecture, or sometimes serres modularity conjecture in order to distinguish it from the many other conjectures serre has made. Jeanpierre serre 1926, a french mathematician active in algebraic geometry, number theory and topology. A counterexample to a conjecture of serre article pdf available in annals of mathematics 1151. Serre river, a tributary of the oise in france serre, campania, a town and comune in the province of salerno in the campania region of. Representations arising from an elliptic curve 11 1. A stronger version of this conjecture specifies the weight and level of the modular form.