Algebraic Geometry

Download E-books To an Effective Local Langlands Correspondence (Memoirs of the American Mathematical Society) PDF

Enable $F$ be a non-Archimedean neighborhood box. allow $\mathcal{W}_{F}$ be the Weil team of $F$ and $\mathcal{P}_{F}$ the wild inertia subgroup of $\mathcal{W}_{F}$. permit $\widehat {\mathcal{W}}_{F}$ be the set of equivalence periods of irreducible soft representations of $\mathcal{W}_{F}$. enable $\mathcal{A}^{0}_{n}(F)$ denote the set of equivalence sessions of irreducible cuspidal representations of $\mathrm{GL}_{n}(F)$ and set $\widehat {\mathrm{GL}}_{F} = \bigcup _{n\ge 1} \mathcal{A}^{0}_{n}(F)$. If $\sigma \in \widehat {\mathcal{W}}_{F}$, enable $^{L}{\sigma }\in \widehat {\mathrm{GL}}_{F}$ be the cuspidal illustration matched with $\sigma$ through the Langlands Correspondence. If $\sigma$ is completely wildly ramified, in that its limit to $\mathcal{P}_{F}$ is irreducible, the authors deal with $^{L}{\sigma}$ as identified. From that start line, the authors build an particular bijection $\mathbb{N}:\widehat {\mathcal{W}}_{F} \to \widehat {\mathrm{GL}}_{F}$, sending $\sigma$ to $^{N}{\sigma}$. The authors examine this "naive correspondence" with the Langlands correspondence and so in achieving a good description of the latter, modulo the utterly wildly ramified case. A key instrument is a unique operation of "internal twisting" of an appropriate illustration $\pi$ (of $\mathcal{W}_{F}$ or $\mathrm{GL}_{n}(F)$) by means of tame characters of a tamely ramified box extension of $F$, canonically linked to $\pi$. The authors convey this operation is preserved via the Langlands correspondence.

Show description

Read Online or Download To an Effective Local Langlands Correspondence (Memoirs of the American Mathematical Society) PDF

Similar Algebraic Geometry books

Fractured Fractals and Broken Dreams: Self-Similar Geometry through Metric and Measure (Oxford Lecture Series in Mathematics and Its Applications)

Fractal styles have emerged in lots of contexts, yet what precisely is a trend? How can one make exact the constructions mendacity inside items and the relationships among them? This booklet proposes new notions of coherent geometric constitution to supply a clean method of this established box. It develops a brand new notion of self-similarity known as "BPI" or "big items of itself," which makes the sector a lot more straightforward for individuals to go into.

The Arithmetic of Elliptic Curves (Graduate Texts in Mathematics)

The speculation of elliptic curves is special via its lengthy historical past and via the range of the equipment which have been utilized in its research. This publication treats the mathematics strategy in its smooth formula, by using simple algebraic quantity concept and algebraic geometry. Following a short dialogue of the mandatory algebro-geometric effects, the booklet proceeds with an exposition of the geometry and the formal team of elliptic curves, elliptic curves over finite fields, the complicated numbers, neighborhood fields, and worldwide fields.

A First Course in Modular Forms (Graduate Texts in Mathematics, Vol. 228)

This ebook introduces the idea of modular types, from which all rational elliptic curves come up, with an eye fixed towards the Modularity Theorem. dialogue covers elliptic curves as advanced tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner concept; Hecke eigenforms and their mathematics houses; the Jacobians of modular curves and the Abelian forms linked to Hecke eigenforms.

Extra resources for To an Effective Local Langlands Correspondence (Memoirs of the American Mathematical Society)

Show sample text content

Rated 4.59 of 5 – based on 20 votes