Bloch group
WebApr 8, 2024 · Eric Bloch is an assistant professor in the Department of Chemistry and Biochemistry at the University of Delaware. Research in his group focuses on the design, synthesis, and characterization of novel porous materials for applications related to energy, the environment, and human health. Webthe Bloch-Kato conjecture, that should be equivalent, but for which a proof of their equivalence requires using more basic, or level-1, but yet unproved and certainly very …
Bloch group
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In mathematics, the Bloch group is a cohomology group of the Bloch–Suslin complex, named after Spencer Bloch and Andrei Suslin. It is closely related to polylogarithm, hyperbolic geometry and algebraic K-theory. See more Let K be a field and define $${\displaystyle \mathbb {Z} (K)=\mathbb {Z} [K\setminus \{0,1\}]}$$ as the free abelian group generated by symbols [x]. Abel's functional equation implies that D2 vanishes on the subgroup D(K) of … See more Via substituting dilogarithm by trilogarithm or even higher polylogarithms, the notion of Bloch group was extended by Goncharov (Goncharov 1991) and Zagier (Zagier 1990). It is … See more If c denotes the element $${\displaystyle [x]+[1-x]\in \operatorname {B} _{2}(K)}$$ and the field is infinite, Suslin proved (Suslin 1990) the element c does not depend on the … See more The Bloch-Wigner function $${\displaystyle D_{2}(z)}$$ , which is defined on $${\displaystyle \mathbb {C} \setminus \{0,1\}=\mathbb {C} P^{1}\setminus \{0,1,\infty \}}$$ , has the following meaning: Let $${\displaystyle \mathbb {H} ^{3}}$$ be … See more WebMar 21, 2024 · We prove that the pre-Bloch group of the function field of E can be generated by the functions of degree not higher than 3. We apply this result to the elliptic dilogarithm function defined by Spencer Bloch.
WebIn particular, elements of the Bloch group $B(F)$ can be written down as linear combinations of symbols $[x], x\in F^\times\setminus\{1\}$ satisfying certain relations. … WebJun 12, 2024 · Let be an elliptic curve over an algebraically closed field of characteristic 0. We prove that the pre-Bloch group of the function field of can be generated by the functions of degree not higher than 3. We apply this result …
WebNov 25, 2024 · Bloch wavefunctions oscillate off to infinity, so the expected position (i.e. your integral before taking the derivative) is not well-defined. It therefore seems ill-suited to try to define a velocity based on the change in the expected position. This definition is a very classical one: It describes how your measurements evolve with time. Webway to de ne the Bloch group which agrees with Suslin’s group up to 2-torsion. In this paper, we will study an invariant of the Bloch group whose values are units in F n …
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