Linear independence of monomials of multizeta values in positive characteristic

Abstract

In this paper, we study transcendence theory for Thakur multizeta values in positive characteristic. We prove an analogue of the strong form of Goncharov's conjecture. We also establish the same result for Carlitz multiple polylogarithms at nontrivial algebraic points.

19 pages; v2: minor corrections on graded algebras are made; v3: minor revision; v4: the last section consists of the last two sections of v3; final version to appear in Compositio Mathematica

References in corpus (3)

• Multizeta values for F_q[t], their period interpretation and relations between them
• Algebraic independence of periods and logarithms of Drinfeld modules (with an appendix by Brian Conrad)
• Relations between multizeta values in characteristic p

Cited by in corpus (21)

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• Alternating multizeta values in positive characteristic
• Analytic continuation of multiple polylogarithms in positive characteristic
• On multiple polylogarithms in characteristic $p$: $v$-adic vanishing versus $\infty$-adic Eulerianness
• Hopf algebras and multiple zeta values in positive characteristic
• Integrality of $v$-adic multiple zeta values
• Universal Families of Eulerian Multiple Zeta Values in Positive Characteristics
• On lower bounds of the dimensions of multizeta values in positive characteristic
• Anderson-Thakur polynomials and multizeta values in positive characteristic
• Algebraic independence of the Carlitz period and the positive characteristic multizeta values at n and (n,n)
• On finite Carlitz multiple polylogarithms
• A $t$-motivic interpretation of shuffle relations for multizeta values
• Trivial multiple zeta values in Tate algebras
• Algebra structure of multiple zeta values in positive characteristic
• Alternating variants of multiple poly-Bernoulli numbers and finite multiple zeta values in characteristic 0 and p
• Analytic continuation of Kochubei multiple polylogarithms and its applications
• Linear relations among algebraic points on tensor powers of the Carlitz module
• On a Conjecture of Gezmis and Pellarin