SKU: 74945048371

Derived Langlands

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Derived LanglandsThe Langlands Programme is one of the most important areas in modern pure mathematics. The importance of this volume lies in its potential to recast many aspects of the programme in an entirely new context. For example, the morphisms in the monomial category of a locally p adic Lie group have a distributional description, due to Bruhat in his thesis. Admissible representations in the programme are often treated via convolution algebras of

The Langlands Programme is one of the most important areas in modern pure mathematics. The importance of this volume lies in its potential to recast many aspects of the programme in an entirely new context. For example, the morphisms in the monomial category of a locally p-adic Lie group have a distributional description, due to Bruhat in his thesis. Admissible representations in the programme are often treated via convolution algebras of distributions and representations of Hecke algebras. The monomial embedding, introduced in this book, elegantly fits together these two uses of distribution theory. The author follows up this application by giving the monomial category treatment of the Bernstein Centre, classified by Deligne-Bernstein-Zelevinsky.

This book gives a new categorical setting in which to approach well-known topics. Therefore, the context used to explain examples is often the more generally accessible case of representations of finite general linear groups. For example, Galois base-change and epsilon factors for locally p-adic Lie groups are illustrated by the analogous Shintani descent and Kondo-Gauss sums, respectively. General linear groups of local fields are emphasized. However, since the philosophy of this book is essentially that of homotopy theory and algebraic topology, it includes a short appendix showing how the buildings of Bruhat-Tits, sufficient for the general linear group, may be generalised to the tom Dieck spaces (now known as the Baum-Connes spaces) when G is a locally p-adic Lie group.

The purpose of this monograph is to describe a functorial embedding of the category of admissible k-representations of a locally profinite topological group G into the derived category of the additive category of the admissible k-monomial module category. Experts in the Langlands Programme may be interested to learn that when G is a locally p-adic Lie group, the monomial category is closely related to the category of topological modules over a sort of enlarged Hecke algebra with generators corresponding to characters on compact open modulo the centre subgroups of G. Having set up this functorial embedding, how the ingredients of the celebrated Langlands Programme adapt to the context of the derived monomial module category is examined. These include automorphic representations, epsilon factors and L-functions, modular forms, Weil-Deligne representations, Galois base change and Hecke operators.

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SKU: 74945048371

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Jennifer
Bozeman, US
★★★★★ 5
My dog LOVES to destroy these
Size: For Medium and Large Breed, Color: 6 Pack, Size: For Medium and Large Breed, Color: 6 Pack
I have a black lab/pitbull mix. She is a very destructive puppy when it comes to her toys. I have tried the "indestructible" toys but they were never indestructible enough and my pup didn't enjoy them. But these... lol. When she gets a new one from the box she loves playing tug of war, playing with the squeakers in the head and the tail (to a nauseating degree), and proudly prances around with her new toy to show everyone. But once that phase passes she gets down to business, tearing at it until she gets the squeakers and crinkly paper out. Thankfully she has no interest in the inner parts of this toy, so once she's done with it I just pick up the squeakers and paper/plastic to throw them out, then it becomes a tug of war toy again until it's time for the "stuffy graveyard". Then we start all over again with a new one (the lifespan is between 3 to 14 days). I've purchased this product 7 times already and will continue to purchase more as long as my doggo loves them. If you've made it this far, sadly these toys can be destroyed if you have a power chewer like my pup, but these toys are cheap by comparison to the "indestructible" toys so they are easily replaceable and don't break the bank. These can be great toys for the right dog.
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Reviewed in the United States on August 23, 2024
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Jodie G
Alexandria, US
★★★★★ 4
Well made and great for tug of war with the dogs
Size: For Medium and Large Breed, Color: 3 Pack
The puppies love these toys. I have no idea what the blue one is supposed to be but they are very cute and seem to be holding up well.
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Reviewed in the United States on June 11, 2026
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RoJo
Bozeman, US
★★★★★ 5
Great non stuffed toys. My dogs love them!
Size: For Medium and Large Breed, Color: 3 Pack
My 2 mini schnauzers LOVE these toys! I LOVE them for several reasons. They is no stuffing inside they can rip open and swallow. There is no strings attached to it like other dog toys that my younger schnauzer loves to pull apart and eat. They play tug of war with them, and so far have held up great. They are a squeeke toy, which the dogs love...me, not so much, but I definitely put up with it. Highly recommend these!
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Reviewed in the United States on April 5, 2026
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Amazon Customer
Fort Morgan, US
★★★★★ 5
Your dogs will love them!
Size: For Medium and Large Breed, Color: 6 Pack
I’m giving this five stars because it was exactly what they claimed it would be. The only negative is our small Papillon tore these to shreds. perhaps, all cloth style toys would be the same.
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Reviewed in the United States on February 28, 2026
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Michael J. Labus
West Palm Beach, US
★★★★★ 3
Not advertised for chewers and it isn’t.
Size: For Medium and Large Breed, Color: 5 Pack
As a play toy for tugging and fetching it would be fantastic. Chew toy? Not so much. In five minutes our 9 month old English Springer Spaniel tore off a foot and started eating the cellophane. Took it from him and removed the cellophane from the leg and trimmed the shredded foot. Gave it back and he chewed off an ear and started on the neck. Had to throw it out. It’s a shame because the price was good, the characters are cute and the squeaker is loud and generates excitement. For non-chewers I highly recommend. For chewers, look elsewhere.
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Reviewed in the United States on April 6, 2026

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