Download Arithmetic of p-adic Modular Forms by Fernando Q. Gouvea PDF

By Fernando Q. Gouvea

ISBN-10: 3540189467

ISBN-13: 9783540189466

ISBN-10: 3540388540

ISBN-13: 9783540388548

The critical subject of this study monograph is the relation among p-adic modular varieties and p-adic Galois representations, and particularly the speculation of deformations of Galois representations lately brought by means of Mazur. The classical idea of modular kinds is thought identified to the reader, however the p-adic idea is reviewed intimately, with considerable intuitive and heuristic dialogue, in order that the publication will function a handy aspect of access to investigate in that zone. the implications at the U operator and on Galois representations are new, and may be of curiosity even to the specialists. a listing of extra difficulties within the box is incorporated to steer the newbie in his study. The publication will therefore be of curiosity to quantity theorists who desire to find out about p-adic modular kinds, major them quickly to attention-grabbing learn, and likewise to the experts within the subject.

Show description

Read or Download Arithmetic of p-adic Modular Forms PDF

Similar algebraic geometry books

The Geometry of Moduli Spaces of Sheaves

Now again in print, this very popular booklet has been up-to-date to mirror contemporary advances within the thought of semistable coherent sheaves and their moduli areas, which come with moduli areas in confident attribute, moduli areas of critical bundles and of complexes, Hilbert schemes of issues on surfaces, derived different types of coherent sheaves, and moduli areas of sheaves on Calabi-Yau threefolds.

Spaces of Homotopy Self-Equivalences: A Survey

This survey covers teams of homotopy self-equivalence periods of topological areas, and the homotopy form of areas of homotopy self-equivalences. For manifolds, the total team of equivalences and the mapping type team are in comparison, as are the corresponding areas. incorporated are tools of calculation, a number of calculations, finite iteration effects, Whitehead torsion and different parts.

Galois Theory of Difference Equations

This publication lays the algebraic foundations of a Galois concept of linear distinction equations and exhibits its dating to the analytic challenge of discovering meromorphic capabilities asymptotic to formal suggestions of distinction equations. Classically, this latter query used to be attacked by means of Birkhoff and Tritzinsky and the current paintings corrects and tremendously generalizes their contributions.

Extra resources for Arithmetic of p-adic Modular Forms

Example text

Since for every n there are maps M ( B / p n B , kn, N;r) -~ M ( B / p " B , k , . N ; 1 ) , taking the inverse limit gives a map M(B, X(i,k), N; r) , M(B, X(,,k), N; 1). It is not clear that this map is an inclusion, because the maps modulo p'~ are not injective. 1 Let the spaces M(B,X(i,~),N;r) and the maps M(B,x(~,k),N;r) , M(B, X(i,k), N; 1) be defined as above. Are the maps c~ inclusions? In other words, can we think of overconvergent forms of weight (i,k) (as defined above) as a certain kind of p-adic modular forms of weight (i, k) ?

P We claim there is an injection D ~ V ( B , N). To see this, let ~" E B be a uniformizer, and let f = ~ f~ E D, where fi E M(K, Np ~',i). T h e n we have f(q) E B[[q]], and, for some n, 7r'~f E ~ M(B,i, Np~), hence ~r"f E V. Then, since (Tr'~f)(q) = 7r'~f(q), f(q) B((q))/V. 1 above), it follows t h a t there exists ] E V such t h a t ](q) = f(q). Hence we m a y define ot D f ,--+ , , V ] . 12) Note t h a t the injectivity follows at once from the equality of the q-expanslons, since B is flat over Zp.

This allows us to define "slope a eigenspaces" for U which generalize (the integral weight case of) Hida's space of "ordinary p-adic modular forms". This will also show that there are few eigenforms for U outside its kernel, in the precise sense that if we fix the weight of f and the valuation of )~, one gets only a finite dimensional space of overconvergent forms of the given weight with eigenvalues of the given valuation. In contrast, it is clear that, even in the overconvergent case, ker(U) is quite large (in fact, infinite-dimensional), because of the Frobenius endomorphism: given any f E M(B,k,N;r), we have f - F r o b V f C ker(U).

Download PDF sample

Arithmetic of p-adic Modular Forms by Fernando Q. Gouvea


by Jeff
4.5

Rated 4.70 of 5 – based on 27 votes