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Black Cat Weekly #43
Welcome to Black Cat Weekly #43. If this isn’t the best issue we had to date, it’s pretty darn close. Lots of great tales are packed into this one—including not one, but two mystery novels (by Edwin Balmer and Nicholas Carter), three shorter mysteries (including a major new novelet by Robert Lopresti, a great reprint by Victoria Weisfeld, and a solve-it-yourself puzzler from Hal Charles). On the science fiction side, we have an amazing set of stories by Daniel Marcus, Isaac Asimov, George O. Smith, Murray Leinster, and Robert Silverberg. It’s hard to get better than that. Oh, wait—we also have an interview with Robert Varley, courtesy of Darrell Schweitzer. This is another one of h...
Existence of the Sectional Capacity
In the case where the norms are induced by metrics on the fibres of ${\mathcal L}$, we establish the functoriality of the sectional capacity under base change, pullbacks by finite surjective morphisms, and products. We study the continuity of $S Gamma(\overline{\mathcal L})$ under variation of the metric and line bundle, and we apply this to show that the notion of $v$-adic sets in $X(\mathbb C v)$ of capacity $0$ is well-defined. Finally, we show that sectional capacities for arbitrary norms can be well-approximated using objects of finite type.
The Second Chinburg Conjecture for Quaternion Fields
The Second Chinburg Conjecture relates the Galois module structure of rings of integers in number fields to the values of the Artin root number on the symplectic representations of the Galois group. This book establishes the Second Chinburg Conjecture for various quaternion fields.
The Dirichlet Problem for Parabolic Operators with Singular Drift Terms
This memoir considers the Dirichlet problem for parabolic operators in a half space with singular drift terms. Chapter I begins the study of a parabolic PDE modelled on the pullback of the heat equation in certain time varying domains considered by Lewis-Murray and Hofmann-Lewis. Chapter II obtains mutual absolute continuity of parabolic measure and Lebesgue measure on the boundary of this halfspace and also that the $L DEGREESq(R DEGREESn)$ Dirichlet problem for these PDEs has a solution when $q$ is large enough. Chapter III proves an analogue of a theorem of Fefferman, Kenig, and Pipher for certain parabolic PDEs with singular drift terms. Each of the chapters that comprise this memoir has its own numbering system and list
Capacity Theory with Local Rationality
This book is devoted to the proof of a deep theorem in arithmetic geometry, the Fekete-Szegö theorem with local rationality conditions. The prototype for the theorem is Raphael Robinson's theorem on totally real algebraic integers in an interval, which says that if is a real interval of length greater than 4, then it contains infinitely many Galois orbits of algebraic integers, while if its length is less than 4, it contains only finitely many. The theorem shows this phenomenon holds on algebraic curves of arbitrary genus over global fields of any characteristic, and is valid for a broad class of sets. The book is a sequel to the author's work Capacity Theory on Algebraic Curves and contain...
Blowing Up of Non-Commutative Smooth Surfaces
This book is intended for graduate students and research mathematicians interested in associative rings and algebras, and noncommutative geometry.
Frobenius Groups and Classical Maximal Orders
Introduction Lemmas on truncated group rings Groups of real quaternions Proof of the classification theorem Frobenius complements with core index 1 Frobenius complements with core index 4 Frobenius complements with core index 12 Frobenius complements with core index 24 Frobenius complements with core index 60 Frobenius complements with core index 120 Counting Frobenius complements Maximal orders Isomorphism classes of Frobenius groups with Abelian Frobenius kernel Concrete constructions of Frobenius groups Counting Frobenius groups with Abelian Frobenius kernel Isomorphism invariants for Frobenius complements Schur indices and finite subgroups of division rings Bibliography
On Natural Coalgebra Decompositions of Tensor Algebras and Loop Suspensions
This book is intended for graduate students and research mathematicians interested in topology and representation theory.
