Results 1  10
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85
Maximal subgroups of finite groups
 J. Algebra
, 1985
"... What ingredients are necessary to describe all maximal subgroups of the general analysis. finite group G? This paper is concerned with providing such an A good first reduction is to take into account the first isomorphism theorem, which tells us that the maximal subgroups containing a given normal s ..."
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Cited by 45 (5 self)
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What ingredients are necessary to describe all maximal subgroups of the general analysis. finite group G? This paper is concerned with providing such an A good first reduction is to take into account the first isomorphism theorem, which tells us that the maximal subgroups containing a given normal subgroup N of G correspond, under the natural projection, to the maximal subgroups of the quotient group G/N. Let PZ = PQ denote the collection of maximal subgroups of G, and let e * be the subset of those ME?)z with Ker,(M) = 1, where Ker,(M) denotes the largest normal subgroup of G contained in M. Then the first isomorphism theorem allows us to identify +Z with the disjoint union UN,, ms,N. Actually, what we really want to parameterize are the conjugacy classes of maximal subgroups, but this too works well: If
Ramification of local fields with imperfect residue fields
 II, Doc. Math. Extra Volume
"... We define two decreasing filtrations by ramification groups on the absolute Galois group of a complete discrete valuation field whose residue field may not be perfect. In the classical case where the residue field is perfect, we recover the classical upper numbering filtration. The definition uses r ..."
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Cited by 34 (7 self)
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We define two decreasing filtrations by ramification groups on the absolute Galois group of a complete discrete valuation field whose residue field may not be perfect. In the classical case where the residue field is perfect, we recover the classical upper numbering filtration. The definition uses rigid geometry and logstructures. We also establish some of their properties. 1
Quaternionic Distinguished Representations
"... this paper is to compare the notion of being GL(2; A )distinguished with the notion (defined below) of being distinguished with respect to another subgroup of GL(2; A E ). Using a "relative trace formula", Jacquet and Lai [JL] carried out such comparisons in certain cases. To extend their results, ..."
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Cited by 28 (7 self)
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this paper is to compare the notion of being GL(2; A )distinguished with the notion (defined below) of being distinguished with respect to another subgroup of GL(2; A E ). Using a "relative trace formula", Jacquet and Lai [JL] carried out such comparisons in certain cases. To extend their results, one could either develop an extensive theory of orbital integrals for the relative trace formula, as is done in [H3], or give a relative version of the DeligneKazhdan "simple trace formula," in which this theory simplifies. We adopt the latter approach. Another objective of this work is to consider such a comparison and a "relative trace" (or "biperiod summation") formula in the higher rank case. Distinguished representations were introduced in a similar context by Waldspurger [Wa], and in our context by Harder, Langlands and Rapoport [HLR] to study Tate's conjectures [T] on algebraic cycles in the case of Hilbert modular surfaces. Then Lai [L] \Gamma using the comparisons of distinguished representations in [JL]
Homology of affine Springer fibers in the unramified case
, 1994
"... Assuming a certain “purity ” conjecture, we derive a formula for the (complex) cohomology groups of the affine Springer fiber corresponding to any unramified regular semisimple element. We use this calculation to present a complex analog of the fundamental lemma for function fields. We show that the ..."
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Cited by 14 (2 self)
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Assuming a certain “purity ” conjecture, we derive a formula for the (complex) cohomology groups of the affine Springer fiber corresponding to any unramified regular semisimple element. We use this calculation to present a complex analog of the fundamental lemma for function fields. We show that the “kappa ” orbital integral that arises in the fundamental lemma is equal to the Lefschetz trace of the Frobenius acting
On the computation of all extensions of a padic field of a given degree
 Math. Comp
, 2001
"... Abstract. Let k be a padic field. It is wellknown that k has only finitely many extensions of a given finite degree. Krasner has given formulae for the number of extensions of a given degree and discriminant. Following his work, we present an algorithm for the computation of generating polynomials ..."
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Cited by 13 (1 self)
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Abstract. Let k be a padic field. It is wellknown that k has only finitely many extensions of a given finite degree. Krasner has given formulae for the number of extensions of a given degree and discriminant. Following his work, we present an algorithm for the computation of generating polynomials for all extensions K/k of a given degree and discriminant. 1.
A Purity Theorem For The Witt Group
 SFB 343
, 1999
"... . Let A be a regular local ring and K its field of fractions. We denote by W the Witt group functor that classifies quadratic spaces. We say that purity holds for A if W(A) is the intersection of all W(Ap ) ae W(K), where p runs over the height one prime ideals of A. We prove that purity holds for e ..."
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Cited by 11 (5 self)
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. Let A be a regular local ring and K its field of fractions. We denote by W the Witt group functor that classifies quadratic spaces. We say that purity holds for A if W(A) is the intersection of all W(Ap ) ae W(K), where p runs over the height one prime ideals of A. We prove that purity holds for every regular local ring containing a field of characteristic 6= 2. R ' ESUM ' E. Soit A un anneau local r'egulier et K son corps des fractions. Soit W le foncteur groupe de Witt qui classifie les espaces quadratiques. On dit que le th'eor`eme de puret'e vaut pour A si W(A) est l'intersection de tous les W(Ap ) ae W(K), o`u p parcourt les id'eaux premiers de hauteur 'egale `a 1 de A. Nous d'emontrons que le th'eor`eme de puret'e vaut pour tout anneau local r'egulier qui contient un corps de caract'eristique 6= 2. 1. Introduction We briefly review the definitions of quadratic spaces and Witt groups. A very detailed exposition of these topics may be found in [8] and in [9]. Let X be a scheme s...
Periodindex problems in WCgroups I: elliptic curves
 J. Number Theory
, 2005
"... Abstract. Let E/K be an elliptic curve defined over a number field, and let p be a prime number such that E(K) has full ptorsion. We show that the order of the ppart of the ShafarevichTate group of E/L is unbounded as L varies over degree p extensions of K. The proof uses O’Neil’s periodindex obs ..."
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Cited by 11 (7 self)
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Abstract. Let E/K be an elliptic curve defined over a number field, and let p be a prime number such that E(K) has full ptorsion. We show that the order of the ppart of the ShafarevichTate group of E/L is unbounded as L varies over degree p extensions of K. The proof uses O’Neil’s periodindex obstruction. We deduce the result from the fact that, under the same hypotheses, there exist infinitely many elements of the WeilChâtelet group of E/K of period p and index p 2. 1.
Periodindex problems in WCgroups II: abelian varieties
"... We study the relationship between the period and the index of a principal homogeneous space over an abelian variety, obtaining results which, in particular, generalize work of Cassels and Lichtenbaum on curves of genus one. In addition, we show that the ptorsion in the ShafarevichTate group of a ..."
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Cited by 10 (9 self)
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We study the relationship between the period and the index of a principal homogeneous space over an abelian variety, obtaining results which, in particular, generalize work of Cassels and Lichtenbaum on curves of genus one. In addition, we show that the ptorsion in the ShafarevichTate group of a fixed abelian variety over a number field k grows arbitarily large when considered over field extensions l/k of bounded degree. Essential use is made of an abelian variety version of O’Neil’s periodindex obstruction.
Curves of genus two over fields of even characteristic
 Math. Zeitschrift
"... Abstract. In this paper we classify curves of genus two over a perfect field k of characteristic two. We find rational models of curves with a given arithmetic structure for the ramification divisor and we give necessary and sufficient conditions for two models of the same type to be kisomorphic. A ..."
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Cited by 10 (2 self)
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Abstract. In this paper we classify curves of genus two over a perfect field k of characteristic two. We find rational models of curves with a given arithmetic structure for the ramification divisor and we give necessary and sufficient conditions for two models of the same type to be kisomorphic. As a consequence, we obtain an explicit formula for the number of kisomorphism classes of curves of genus two over a finite field. Moreover, we prove that the field of moduli of any curve coincides with its field of definition, by exhibiting rational models of curves with any prescribed value of their Igusa invariants. Finally, we use cohomological methods to find, for each rational model, an explicit description of its twists. In this way, we obtain a parameterization of all kisomorphism classes of curves of genus two in terms of geometric and arithmetic invariants.