On Emerton ’ S

Instructional Conference on Representation Theory and Arithmetic Notes Taken by Mike Woodbury

Goal of Conference 2 1. Matt Emerton: Classical Modular Forms to Automorphic Forms 2 1.1. The Growth Condition 3 1.2. Passage to Representation Theory 4 2. David Nadler: Real Lie Groups 5 2.1. Basic Notions 5 2.2. Examples 5 2.3. Classification 6 2.4. Useful Decompositions 7 3. Jacob Lurie: Lie Theory and Algebraic Groups 8 3.1. Classification 9 4. Jacob Lurie: Representations of algebraic grou...

New species of Habronattus and Pellenes jumping spiders (Araneae, Salticidae, Harmochirina)

The harmochirine jumping spiders include the New World Habronattus, notable for their complex courtship displays, and Pellenes, found throughout the Old World and North America. Five new species of Habronattus and one new species of Pellenes are here described from North America: Habronattus aestus, sp. n., Habronattus chamelasp. n., Habronattus empyrussp. n., Habronattus luminosussp. n., Habro...

Ecosystems, Infrastructure, and the Use of Economics to Influence Decisionmaking

A REINTERPRETATION OF EMERTON’S p-ADIC BANACH SPACES

It is shown that the p-adic Banach spaces introduced by Emerton, are isomorphic to the cohomology groups of the sheaf of continuous Qp-valued functions on a certain space. Some applications of this result are discussed.

On 3-class Groups of Certain Pure Cubic Fields

Let p be a prime number, and let K = Q( 3 √p). Let M = Q(ζ, 3 √p) = Q( √ −3, 3 √p), where ζ is a primitive cube root of unity. Let SK be the 3-class group of K (that is, the Sylow 3-subgroup of the ideal class group of K). Let SM (respectively, SQ(ζ)) be the 3-class group ofM (respectively, Q(ζ)). Since Q(ζ) has class number 1, then SQ(ζ) = {1}. Assuming p ≡ 1 (mod 9), Calegari and Emerton [3, ...