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27 Apr 2016: Automorphy of some residually S5 Galois representations. Chandrashekhar B. Khare and Jack A. Thorne†. April 27, 2016. Abstract. Let F be a totally real field and p an odd prime. We prove an automorphy lifting theorem forgeometric representations

12 Oct 2002: Lemma 1.1 (Proposition 1). If P and Q are linear partial differential op-erators.

5 Jun 2024: A WEISS–WILLIAMS THEOREM FOR SPACES OF EMBEDDINGSAND THE HOMOTOPY TYPE OF SPACES OF LONG KNOTS. SAMUEL MUÑOZ-ECHÁNIZ. ABSTRACT. We establish a pseudoisotopy result for embedding spaces in the line of that of Weiss and Williamsfor

20 Dec 2023: Then there is a bounded K-Banach algebra isomorphism. ()T : A〈/r〉 A〈/r〉op. ... Proof. We apply Lemma 2.2.10 with A = O(X), δ = x B(A), B := A〈/r〉op,b = and f : A B the natural inclusion.

22 Oct 2001: The local. field Fp has ring of integers Op and normalised valuation ordp. ... im δp =. Fp /F. 5p if ordp(λ) 6= 0. Op/O5p if ordp(λ) = ordp(λ.

11 Sep 2017: We say that P is a U-coadmissible (U,V )-bimodule if there is a continuous homomorphism V op EndU(P) with respect toa natural Fréchet structure on EndU(P) defined

21 Aug 2008: Though cast in. category-theoretic language, the result in op. cit. is essentially the inter-denability result of second.

21 Aug 2008: Though cast in. category-theoretic language, the result in op. cit. is essentially the inter-denability result of second.

27 Jun 2007: THE BOUNDARY RIGIDITY PROBLEM IN THE PRESENCEOF A MAGNETIC FIELD. NURLAN S. DAIRBEKOV, GABRIEL P. PATERNAIN, PLAMEN STEFANOV,AND GUNTHER UHLMANN. Abstract. For a compact Riemannian manifold with boundary, endowed witha magnetic potential α, we

2 Jan 2014: mans was to code up what will be products and then give a suitably related op-.

21 Aug 2003: Proof. Assume we have a premonoidal Conway operator (). The Conway op-erator obtained from the trace obtained from () maps f : A U U to(〈π1, π3〉; f ; ); π1.

22 Aug 2008: We have a fun tor ( )? : Cd - (Cd)op with(U;X)? =

22 Aug 2008: We have a fun tor ( )? : Cd - (Cd)op with(U;X)? =

16 Apr 2014: Automorphy lifting for residually reducible l-adic Galois. representations. Jack A. Thorne. April 16, 2014. Abstract. We prove automorphy lifting theorems for residually reducible Galois representations in the settingof unitary groups over CM fields.

29 Jan 2010: INDEX TO SGA 1. INDEX TO SGA 1! " # $ % & $ ' & " ( # ) # # & , -! / #! 0 ' %! 1 2! 3 , -! / #! % / 2 # )! ' #! 4 , -! / #! # ) % & #! 5 # 6 # 7 # / #! # ) % & #! 38 9 % - - # ) # ) : " % / # % & # " #! / -! / #! # ) % & #! 8; < - - & $ % % ' = # = #

22 Jan 2008: Then thereare categories of spaces: the most familiar is Top, the category of topological spaces;but there are many other notions of space, for example [op, Sets], the category ofsimplicial sets

9 Sep 2002: The list does include allsimply-connected rank-one symmetric spaces except CP 2, OP 2 (the Cayley projectiveplane) and the obvious case S2.

29 Jul 2011: ON THE AUTOMORPHY OF l-ADIC GALOISREPRESENTATIONS WITH SMALL RESIDUAL. IMAGE. JACK THORNE. Abstract. We prove new automorphy lifting theorems for essen-tially conjugate self-dual Galois representations into GLn. Existingtheorems require that the

20 Dec 2018: Coding and Cryptography. T. W. Körner. December 20, 2018. Transmitting messages is an important practical problem. Coding theoryincludes the study of compression codes which enable us to send messagescheaply and error correcting codes which ensure

16 Mar 2016: A 2-adic automorphy lifting theorem for unitary groups over CM. fields. Jack A. Thorne. March 16, 2016. Abstract. We prove a ‘minimal’ type automorphy lifting theorem for 2-adic Galois representations of unitarytype, over imaginary CM fields. We